Fallon, sacked by Henry Cecil on Tuesday, also expressed the hope that he would still ride for the Warren Place trainer, for whom he has won three of the four 1999 Classics.
Racecourse rumour was rife that Fallon has been lined up to replace Stevens, said to be in talks with the Thoroughbred Racing Corporation, owners of Oath and horses in California.
Asked whether Stoute had made contact with him, Fallon said: "I would like to work with a stable - I wouldn't like to be freelance - but it is only rumours, really. I haven't been approached by any stable but I would like to ride for a stable."
Stevens, whose union with Stoute has delivered less than it promised amid what has been a quiet summer for Freemason Lodge, confirmed he was involved with talks but would not be specific as to the exact nature. "I really can't make a lot of comment on it," he said. "I will say the speculation is true - there are negotiations going on but at this point I really can't say what is going on. Myself and the boss, Sir Michael, will make an announcement in five or six days."Reuse content