This is a difficult question to answer easily for two overlapping reasons.

Firstly, "empire" is a term is incredibly slippery term for historians to define. Empires are often very complex entities and trying to extrapolate some general features means there is a loss of nuance. For example, Charles Tilly came up with a serviceable definition for empire:

An empire is a large composite polity linked to a central power by indirect rule. The central power exercises some military and fiscal control in each major segment of its imperial domain, but tolerates two major elements of indirect rule: (1) retention or establishment of particular, distinct compacts for the government of each segment; and (2) exercise of power through intermediaries who enjoy considerable autonomy within their own domains in return for compliance, tribute, and military collaboration with the center.

Tilly's definition is quite flexible, but also deliberately quite vague and can be stretched too far. For example, one can use Tilly's definition to label the US's immediate postwar position in Western Europe an empire with economic agreements like Bretton Woods, institutions like NATO, and foreign aid like the Marshall Plan as a instruments of an American imperium. This is one problem with labeling entities like the USSR or the US as empires haphazardly, one you stretch these conceptualizations, the term itself becomes distorted and loses its original meaning.

Secondly, applying the term empire to twentieth-century polities often carries critical overtones. This was particularly true for the USSR, where labeling the Marxist-Leninist state an empire carried with it an additional charge of hypocrisy as Moscow styled itself in its public diplomacy as the world's foremost opponents of imperialism. Cold War-era commentators and historians, who were often highly partisan, frequently described the Soviet Union as an empire as part of a broader assault on the legitimacy of the Soviet experiment. For example, Richard Pipes would label the USSR as a "prison of the peoples," and draw connections to crackdowns in Eastern Europe with discriminatory policies against Central Asians and the Ukrainian famine. For Pipes and his ilk, Soviet anti-imperial ideology was merely a stalking horse for Great Russian hegemony. This condemnatory historiography has meant that discussions of empire and the USSR are often freighted with a degree of politics. Defining the Soviet Union as an empire also gained a degree of legitimacy after the collapse of the USSR as it meshed well with popular notions of imperial collapse and the verdicts of history.

In general, historical scholarship on the Soviet Union does not consider the USSR to be an empire in the formal sense of the definitions as those espoused by Tilly. As such, when historians describe the USSR as an empire, it is often in a very qualified sense. For example, Ronald Suny recently described the USSR as an empire in his recent book Red Flag Unfurled, but noted that his imperial paradigm could also easily apply to modern liberal nation-states like Belgium which have national minorities. Part of the problem with applying the label imperial to the USSR is that Moscow's handling of the multiethnic character of the state it had inherited was decidedly unimperial. The Soviets enacted various policies that often operated against the interests of the Great Russian population. In drawing up the internal borders of the state, the Soviets territorialized ethnicity which created internal republics and other administrative entities to be led by the respective dominant ethnicity (e.g. Ukrainian, Kazakhs, etc.). Inside these new republics, the state facilitated indigenous language instruction, sponsored cultural activities, and, especially in the early years of the USSR, disciplined instances of Great Russian chauvinism. One of the animating policies of the USSR was korenizatsiia (indiginization) which sought to promote native cadres loyal to the Communist Party and the Soviet state. Although the Stalin turn of the 1930s pushed back against korenizatsiia, this idea never really went away throughout the life of the USSR. Entities like the Communist Party, the Komsomol, and the Red Army acted as supranational entities throughout the USSR and were quite prominent social institutions. The planned economy often redistributed industrial and other economic resources in ways that did not benefit the Great Russian core of the RSFSR. Even the Soviet control over postwar Eastern Europe was not as hegemonic as it appeared during the Cold War. Research into the archives of the Warsaw Pact governments has shown that the leaders of the satellite sometimes possessed a greater deal of latitude than prior historiography assumed (one monograph emblematic of this new turn in scholarship in GDR studies has a title that encapsulates this idea: Driving the Soviets Up a Wall).

That being said, although many historians of the Soviet Union today tend to reject or qualify the idea that the USSR was an empire, this does not mean that they do not look towards imperial studies to explain the Soviet experience. For example, korenizatsiia often requires a firm definition of what features exactly constitutes a nationality. Both Francine Hirsch and Yuri Slezkine have uncovered how this process often repackaged older tsarist conceptualizations of an exotic non-European other. Soviet modernization drives in Central Asia often fell back upon older stereotypes, colonial discourses and tropes like the veiled and subordinate status of Muslim women. Similarly, a lot of the monographs on the experience of native cadres has fruitfully mined subaltern studies to explain how non-Great Russians navigated this system. Finally, in terms of great power relations, the Soviet desire to cling to its Eastern European satellite meshes well with how classical empires frequently perceived power in terms of a zero-sum game and fought desperately to retain its power.

That really depends on how one defines an empire. To quote Websters via the [Wikipedia article on Empire](an aggregate of nations or people ruled over by an emperor or other powerful sovereign or government): an Empire is "an aggregate of nations or people ruled over by an emperor or other powerful sovereign or government..."

So does the USSR qualify as this? That is honestly a debate that has ranged since the October Revolution brought the Bolsheviks to power, and has arguably intensified since its collapse. After all, the USSR was comprised of a multitude of different nations and peoples, and they were ruled over by one government (and arguably one person for long periods). However it didn't have an "Emperor," in that the leader was not titled as such nor was the position hereditary, or really codified in how successors were appointed.

That said, I would say that the USSR could be considered an empire, with the caveat that it was in a similar structure. Of course I'm coming from my expertise of looking at national minority groups within the USSR, and so am using the school of thought prevalent in those who research that as well. I'll further cite two influential book titles that I think would support such a position: The Affirmative Action Empire: Nations and Nationalism in the Soviet Union, 1923-1939 by Terry Martin (2001), and Empire of Nations: Ethnographic Knowledge and the Making of the Soviet Union by Francine Hirsch (2005). Of course they are just titles, and meant to catch the eye. But each supports the idea that the Soviet Union was built to develop its people, even the minority non-Russian peoples. This is somewhat in line with what an empire would traditionally be seen as, even if you want to argue that an empire is meant to serve its "titular" people. In this case of course everyone was Soviet, but if you look at the idea of the Russians filling this role (a view that has been challenged in the post-Soviet historiography; the current consensus is that the Soviet Union was not feeding everything to the centre in Moscow, but indeed tried to develop the non-Russians), it is supported as well: Martin notes that after the initial attempts to develop the non-Russians of the USSR, Stalin shifted this and promoted Russianness as the main feature of the Soviet people; while Hirsch's book argues it was the Russians who did the work to promote the various ethnic groups, so they in effect had the lead on that.

So I will conclude by saying that there can be points that both support and refute this question, and it really comes down to how you want to define an empire. I already noted my own leanings on the matter, and would say more often than note the USSR could be called an empire, but I certainly would not totally disagree with the opposite, and indeed could agree to that point as well.