The overwhelming consensus of historians is that Stalin was not planning to attack in summer 1941 and was hoping the Soviet Union would not be caught up in the general war just yet. The German attack caught by him surprise.

The modern incarnation of the theory that Stalin was actually planning to attack that summer and was preempted by Hitler originates with *Viktor Suvorov, Icebreaker: Who Started the Second World War? (1988--that is actually the date of the first Russian edition published in Paris; the first English edition was published in 1990 and is now quite costly). Suvorov is the penname used by Soviet defector Vladimir Bogdanovich Rezun, who'd written a number of books about the contemporary Soviet military and security apparatus using his insider credibility before turning to history, where he's unfortunately just another retired military officer with some things to say but not much evidence to back them up. For the basics of this controversy, I can do no better than refer you to the excellent answer by u/Georgy_K_Zhukov to the frequently asked question of whether the Soviets were planning to attack (though maybe the Marshal or someone else will expand).

As far as I can tell, Beevor like basically all professional historians in the English-speaking world didn't believe it and probably even didn't think it was worth mentioning in Stalingrad (1998). Beevor did research and his research showed that the Soviets were caught by surprise and were not planning an attack of their own--that is the narrative that takes up the first chapters of the book you are reading. Suvorov did not do much research to speak of.

You may be wondering why, if Suvorov published Icebreaker in 1988 or 1990 or so, and Beevor published a major book on the first stages of the Soviet-German war about ten years later, Beevor didn't go ahead and say that contrary to what you may have heard, Stalin wasn't planning to attack.

My impression of the historiography (as someone whose procrastination strategy in college and grad school during the 1990s was to read more East Front books and articles) is that Suvorov's theory was seen as so crazy and unsupported, more akin to a political opinion than a serious historical argument, that such a response was not obligatory when addressing a mass audience in English. Indeed, I think it's accurate to say that in the English-speaking world, Icebreaker was initially regarded as mostly a relic of the Cold War ("Stalin bad! Soviets bad! Germans not so bad!") reminiscent of certain defenses of the Germany's policies in the 1933-45 era than a serious contribution to the study of WWII.

In other words, "Was Stalin planning to attack in summer 1941?" was not quite a frequently asked question in historiography of the Soviet-German war in the mid 1990s. Beevor's putative reader, picking up the book in a bookstore or library, or perhaps receiving it as a present, probably would not have heard that Stalin was going to strike first and so didn't need to be told the he actually wasn't. And that is the book you are reading even though the landscape has changed.

As it turned out, Icebreaker and follow-ups by Suvorov sold well in Germany and the former Soviet Union particularly after a 1992 mass-market edition was published in post-Soviet Russia. They attracted some scholarly support in those countries. Major English-language refutations of Icebreaker were appearing about the time Beevor's Stalingrad did: David M. Glantz, Stumbling Colossus: The Red Army on the Eve of War (1998) and Gabriel Gorodetsky, Grand Delusion: Stalin and the German Invasion of Russia (1999); see also the article by Uldricks cited in the FAQ answer linked above. (Glantz, by the way, is a retired military officer with a lot to say and a stack of evidence to back it up.)

So by the time Beevor wrote his general history The Second World War (2012), he did feel the need to confront the Icebreaker controversy. Therein he describes the position that Stalin was the real would-be aggressor as one held by "conspiracy theorists" including Suvorov. He cites a number of refutations giving particular weight to the work of Russian scholars. (Beevor does allow that Stalin may have been planning to attack later, like that winter, but this is a far cry from Suvorov's claims of an imminent attack that Barbarossa disrupted.)

I hope this is helpful in pointing toward resources on that theory you've heard about as well as explaining why Beevor didn't address the issue.