The intention was to work through "associates" of the two stars to lure the Kennedys -- as well as Peter Lawford, their brother-in-law, and fellow member of Sinatra's "rat pack" -- into actions they would regret.
An FBI statement accompanying the papers said: "(The file) contains report of a rumour from an informant suggesting that elements of the Mafia wanted to attack the character of Edward and Robert Kennedy and their brother-in-law Peter Lawford by working through associates of Frank Sinatra to compromise them at a New York party. Both Frank Sinatra and Marilyn Monroe were to be involved."
After looking into the claims, the FBI is said to have decided the information was not "solid" enough and no other mention of it appears. The plot is thought to have fizzled out, but it is consistent with other accounts of the extraordinary links between America's greatest political dynasty, the country's biggest stars and organised crime.
Monroe, who died in 1962, allegedly had affairs with both Robert Kennedy and John F Kennedy, the former president who was assassinated in 1963. It has previously been claimed that she passed on "pillow talk" from Robert Kennedy to Sinatra, who in turn passed it on to Mafia friends.
As attorney general, Robert Kennedy opened several investigations into the Mafia, which it may have felt warranted a measure of retribution.
Papers released this year by the library of former president Richard Nixon showed that in the early 1970s he discussed with aides the possibility of discrediting Kennedy by leaking news of his infidelities.
The 2,352 pages of FBI documents -- dated from 1961 to 1985 and released under a freedom of information request -- showed the late senator received a flow of death threats even after his last attempt at the presidency failed in 1980.
They showed that Sirhan Sirhan, the man who shot Robert Kennedy dead in 1968, tried to recruit a fellow prisoner about to be released to kill Edward Kennedy, offering him "a million dollars and a car".
Death threats originated from multiple sources, including individuals and members of radical groups such as the Ku Klux Klan, 'Minutemen' organisations, and the National Socialist White People's Party.
The files also showed that the FBI did not investigate Edward Kennedy's car crash on Chappaquiddick Island off the coast of Massachusetts. It knew about the incident immediately and colluded in initially keeping his identity secret. The senator's 19-year-old passenger, Mary Jo Kopechne, drowned in the crash, which ended his presidential ambitions.
In his memoir 'True Compass', Kennedy, who died last August aged 77, wrote that his actions on Chappaquiddick were "inexcusable". (© Daily Telegraph, London)