Savage is expected to leave Manchester United during the ongoing summer transfer window, with the Red Devils open to both loan and permanent offers.
He has generated substantial interest in the Championship, with Swansea amongst the clubs claimed to be keen on him.
However, Savage will not be heading to Wales, with Swansea not chasing his signature this summer.
A host of clubs have looked at Savage, with Reading considered to be strong contenders to sign him, even though that would mean a drop into League One.
Michael Duff replaced the recently-departed Russell Martin at Swansea and he is trying to revamp the squad, but Savage will not be joining.
Savage joined Forest Green Rovers on loan in the second half of the season, but could not help them avoid relegation.
The midfielder will look to make sure he is clocking regular game time wherever he moves this summer.