Not quite — and, to be clear before I go any further: there is no credible evidence that Kennedy was ever a Soviet sympathiser, KGB asset or contact, agent of influence or anything else in that vein.

Now, to the kernel of truth at the heart of this claim: it does appear to be true that Kennedy quietly attempted in early 1983 to open a dialogue with Soviet general secretary Yuri Andropov.

The key source for this claim is a lengthy memo from Viktor Chebrikov, the chairman of the KGB, to Andropov. In the letter, dated 14 May 1983, Chebrikov reports that former US senator and Kennedy associate John Tunney had arrived in Moscow the previous week — and that he bore a message from Kennedy. (It's not entirely clear to whom Tunney was speaking; whether it was the KGB, or another apparatchik.)

In the memo, Chebrikov reports that Kennedy was deeply concerned at Reagan's belligerent posture, particularly on the subject of nuclear weapons disarmament, and that he was equally worried about weak Democratic opposition enabling Reagan to win re-election in 1984. He writes that Kennedy requested a personal invitation to Moscow for a meeting with Andropov, and suggested that Andropov participate in televised interviews with the American media in an effort to rehabilitate the USSR's image in the eyes of the American public. Lastly, and most controversially, Chebrikov claimed that Tunney had informed him of Kennedy's intention to run for president in 1988 — and hinted that a new Kennedy administration would take a substantially more conciliatory line than Reagan's.

A British journalist, Tim Sebastian, discovered the Chebrikov letter in a Russian archive in 1992, summarising its contents a report for The Times. Tunney confirmed to Sebastian that he had made repeated visits to the USSR as a go-between for American legislators. He doesn't specifically confirm that Kennedy was one of the people for whom he acted as an informal envoy — but, tellingly, he doesn't deny it either.

What is at issue is whether Chebrikov's account of the overture is accurate. Tunney told Sebastian it was "bullshit", alleging that Kennedy had no intention of running in 1988, that electoral politics weren't discussed, and that he didn't give the Soviets advice on staging a PR blitz in the United States.

In 2006, the conservative historian Paul Kengor published the letter in its entirety in his book The Crusader: Ronald Reagan and the Fall of Communism, bringing it to a wider American audience for the first time. The Chebrikov letter and the electrifying implication that Kennedy had attempted to work with the Soviets to undercut the Reagan administration was a sensational revelation for American conservatives, who despised Kennedy (understandably, given his position as one of the icons of 20th century Democratic liberalism.)

Even if the letter is an accurate portrayal of the Tunney approach, it doesn't really show any impropriety; at worst, it looks like cynical politicking. When this story comes up in conversations about Kennedy, though, there's usually some innuendo; the implication from the right is that back-channeling with the Soviets was a borderline treasonous activity.

The short version is that we just don't know whether Chebrikov or Tunney's account is accurate. But the authenticity of the memo itself has never been debunked, and it's perfectly possible that the truth is somewhere in the middle. Certainly, it's not a stretch to believe that an account filtered through the KGB bureaucracy may have been manipulated before it ever made its way to Andropov's desk — just as it's no stretch to believe that Tunney might dissemble or downplay embarrassing revelations about a close friend and longstanding political ally.