Gayle featured sporadically under Alan Pardew last season and scored 10 times in his 29 appearances for the Eagles.
However, the ambitious Bristol City are keen to dominate in the Championship this season and have submitted the giant bid in order to acquire Gayle, a player they believe will help them gain promotion to the Premier League.
The bid is reported to have been accepted but the Daily Mail reports that Gayle himself is reluctant to play in the Championship and is set to reject the move.
City boss Steve Cotterill confirmed the bid but told his club's official website that he was unsure of what was going to happen next.
Cotterill said: "We've had a bid accepted and that's as far as it's gone.
"We need to speak to the player and his agent. I don't think anything has changed whilst we've been playing so maybe we'll know more on Wednesday."