The 'Tractor Boys' are looking for a replacement for Martyn Waghorn, who has completed a move to Derby County.
Windass bagged 18 goals for the 'Gers' last season across all competitions, which has tempted Paul Hurst into making a bid for the 24-year-old.
Rangers are reportedly yet to make a decision on the bid; Windass signed a new contract with the Scottish side in February and manager Steven Gerrard would need a successor lined up for the attacker before Thursday's deadline.
The 'Gers' have also been linked with a move for Dinamo Zagreb's Bosnian striker Armin Hodzic, who has scored 68 goals in 160 matches across all competitions for the Croatian side.