Kevin Blackwell is looking into the possibility of either a free transfer or loan deal for the player.
Flitcroft broke into the Manchester City first team in 1992 and he made the move across Lancashire for £3.2m in March 1996.
His debut at Rovers lasted just four minutes, a clash with a defender seeing him red-carded. But it's that fiery nature that Leeds may need to make a concerted effort for promotion this season.