Southern, who penned the Dr. Strangelove script for the late director, wrote to Kubrick complimenting him on casting Ryan O'Neal in his 1975 film Barry Lyndon, recalling an encounter with the movie star at a Jagger party.
The screenwriter told Kubrick he once stumbled in on a sex session between O'Neal and Mick Jagger's then-wife Bianca at the couple's home in London.
The letter, which has been obtained by editors at Man of the World magazine and will be published later this month (Sep15), suggest Southern, who also wrote the Easy Rider screenplay, was a guest at Jagger's London home and accidentally walked in on the Love Story star and the rocker's model wife in the throes of passion.
An extract obtained by the New York Post's Page Six reads: "I had the pleasure of meeting R. O'Neal... while we were both guests in the home of rock-star Mick Jagger... and his charming wife, Bianca - to whom, unless I am very much mistaken, young O'Neal was putting his stout wood in a most forceful manner.
"In fact, Stan, I would be less than candid if I failed to mention how I walked into the room one afternoon to find them going at it like a pair of maddened wart-hogs."
He adds, "O'Neal's coarse animal member (was working) with such tumultuous abandon as to literally smash the darling girl against the sideboard at the very mo (moment) when yrs tly (yours truly) was pouring himself a short one (drink)!"
Bianca revealed in 1977 that she'd had a two-year fling with the actor.
The Jaggers split in 1978.
Representatives for Bianca Jagger and O'Neal have yet to comment on the contents of Southern's letter to Kubrick.
Southern died in 1995.