The hosts went 2-1 up with one to play in the series after coming from behind to win the third Test by 141 runs at Edgbaston on Sunday.
Rashid has been in and around the England squad all season, but is still waiting to play on home soil after making all his three career Test appearances against Pakistan in the United Arab Emirates last year.
But, with England set to tour Bangladesh and India — where pitches often provide plenty of turn for slow bowlers — later this year, Rashid could be called up at The Oval in south London as a second spinner alongside Moeen Ali.
During last year’s Ashes, Australia off-spinner Nathan Lyon took four wickets in his side’s consolation win at The Oval.
Asked if England were tempted to pick Rashid for the fourth Test, which starts on Thursday, Bayliss replied: “Very. We saw last year at The Oval, the wicket had a bit in it for everyone.
“Lyon bowled very well there, got some spin and bounce.”
Rashid took seven for 61 in champions Yorkshire’s County Championship win over Warwickshire last week, after being released from England’s squad.
Bayliss added: “I’ve thought Rashid’s been a chance for the last two or three Tests that we’ve played.
“At some stage, he will get an opportunity.”
Ali made his name as a top-order batsman before being handed the position of England frontline off-spinner following the retirement of Graeme Swann.