The Leeds academy product has had limited minutes in the first team this season and was on the bench in their FA Cup win over Cardiff City on Wednesday night.
Wilfried Gnonto’s emergence this season and the signing of Georginio Rutter this month have further pushed him down the pecking order.
Leeds are considering loaning him out before the end of the window and several clubs in the Championship are interested in him.
And it has been claimed that Swansea are amongst the teams who have a strong interest in signing Gelhardt.
The Welsh club are eleventh in the league table but are just three points behind the teams in the playoff spots.
Swansea are looking to bring in a striker whose goals could help them in their bid to get promoted.
Leeds are currently debating whether to let Gelhardt leave on loan or keep him around in the squad for the rest of the season.
Sunderland are also interested in him and are reportedly looking to use Amad Diallo’s development as leverage in their efforts to sign the striker.