A repost of an earlier answer I wrote:

There actually was a movement to replace the Union of Soviet Socialist Republics with a more democratic union, and this was actually one of the sticking points that ultimately led to the dissolution.

The idea that Gorbachev undertook starting in late 1990 was to replace the 1922 Union Treaty forming the Soviet Union with a new treaty that would effectively refound the USSR as a "Union of Sovereign States". The process by which he negotiated this with most of the republican leaders was called the "Novo-Ogarovo Process" (named after the Moscow suburb where the talks were held), and the general idea was that the republics would receive greater sovereignty/autonomy, and the Union as a whole would maintain a common presidency (ie, Gorbachev), foreign policy and military. Almost like a supercharged EU.

The background here is that after the end of the Communist Party's Constitutional monopoly on power and subsequent republican elections in 1990, the Soviet Socialist Republics, even those controlled by the Communist Party cadres, began a so-called "war of laws" with the Soviet federal government, with almost all republics declaring "sovereignty". This was essentially a move not so much at complete independence but as part of a political bid to renegotiate powers between the center and the republics.

Gorbachev in turn agreed to this renegotiation, and began the so-called "Novo-Ogaryovo Process", whereby Soviet representatives and those of nine republics (ie, not the ones who boycotted the referendum) met from January to April 1991 to hash out a treaty for a new, more decentralized federation to replace the USSR (the proposed "Union of Soviet Sovereign Republics" is best understood as something that was kinda-sorta maybe like what the EU has become, in terms of it being a collection of sovereign states that had a common presidency, foreign policy and military).

A referendum was held in the USSR on March 17, 1991 as a means by Gorbachev to demonstrate popular support for a new treaty. The referendum was not held in six of the fifteen republics (Lithuania, Latvia, Estonia, Moldova, Georgia and Armenia). All of these except Armenia had basically elected non-communist governments in republican elections the previous year, and Lithuania had even declared independence in March 1990. Latvia and Estonia held referenda endorsing independence two weeks before the Soviet referendum, and Georgia held a similar referendum two weeks after. So even holding the vote was a fractured, not Union-wide affair.

It's also important to note the language of the referendum was for a renewed federation of equal sovereign republics. This may sound like a platitude, but effectively what it means is "do you support President Gorbachev renegotiating a new union treaty to replace the 1922 USSR Treaty?"

Even the passage of the referendum in the participating nine republics wasn't exactly an unqualified success: Russia and Ukraine saw more than a quarter of voters reject the proposal, and Ukraine explicitly added wording to the referendum within its borders that terms for the renegotiated treaty would be based on the Ukrainian Declaration of State Sovereignty, which stated that Ukrainian law could nullify Soviet law.

In any event, the treaty was signed by the negotiating representatives on April 23, and went out to the participating republics for ratification (Ukraine refused to ratify), and a formal adoption ceremony for the new treaty was scheduled to take place on August 20.

That never happened, because members of Gorbachev's own government launched a coup the previous day in order to prevent the implementation of the new treaty. The coup fizzled out after two days, but when Gorbachev returned to Moscow from house arrest in Crimea, he had severely diminished power, and Russian President Boris Yeltsin (who publicly resisted the coup plot) had vastly increased power, banning the Communist Party on Russian territory, confiscating its assets, and pushing Gorbachev to appoint Yeltsin picks for Soviet governmental positions.

In 1990, during the so-called "War of Laws" between the republics and Gorbachev's Soviet center, Yeltsin was very much in favor of the republics exercising their sovereignty and working together as allies. However, once Yeltsin had maneuvered Gorbachev into the sidelines as the still-existing-but-ineffective Soviet President, he actually became the single most powerful political figure in the still-existing Union, and as such found a new love in keeping the Union together, in some form.

While in the immediate aftermath of the August 19-22 coup attempt against Gorbachev (and Yeltsin's "counter-coup" thereafter) Yeltsin was fine with publicly recognizing the independence of the Baltic states, the declarations of independence by other SSRs, led by Ukraine, were something of a shock to him and the Russian republican government: Ukraine's legislature voted for independence on August 24 (to be confirmed in a referendum scheduled for December), Belarus declared independence on the 25th, Moldova on the 26th, Azerbaijan on the 30th, Kyrgyzstan on Sept 1st, and Uzbekistan on the 2nd. The practical effect of these declarations was that, where the republics' declarations of "sovereignty" in 1990 prioritized republican law over union law, these declarations effectively nullified union law altogether.

The Ukrainian declaration of independence was read aloud (in Russian) at an August 26 meeting of the Soviet parliament, and met with very hostile responses. Perhaps predictably, Gorbachev's face turned red and he stormed out. Yet more surprisingly, Russian democratic reformers rose to also speak out against republican independence. Anatolii Sobchak, the reformist mayor of St. Petersburg (and future mentor to Putin) denounced independence as a means to save "national communist structures, but with a new face", and worried about nuclear anarchy. Others spoke of the fear these independence declarations would do to democracy, and the possibility of border wars.

Ukraine finally held its referendum on the declaration of independence on December 1. The result was a profound shock to both Gorbachev and Yeltsin - 92% of voters supported independence in 84% turnout, and every region supported the measure with a majority of voters (albeit in Sevastopol it was 57% and in Crimea it was 54%).

When Yeltsin went to meet with Leonid Kravchuk, elected Ukrainian president the same day of the referendum, and Belarusian leader Stanislav Shushkevich at Belavezha, Yeltsin still had some hopes of salvaging a Union, but Kravchuk was uninterested - the Ukrainians wanted full independence, and Yeltsin was in turn not interested in a Union that didn't include Ukraine, as he feared such a union would give too much relative power to the barely-ex-communists in the Central Asian republics. The most that could be agreed upon in the Belavezha Accords was the formal dissolution of the USSR (on the premise that Ukraine, Belarus and Russia were the remaining founding republics of the 1922 union) and replacing it with the Commonwealth of Independent States, which 8 other republics formally endorsed in Alma-ata Kazakhstan in December 21. In both meetings, the republican officials affirmed the republican borders and refused recognition of any secessionist movements.