The Daily Express claim United want to sign the 21-year-old until the end of the season.
The Arabs could face competition though with Fleetwood Town apparently also interested.
Rossiter has had a torrid time with injuries and a loan move would be a great chance to get games.
So far this season, he has only managed five appearances.
United are pushing for promotion back to the Premiership this season – currently sitting three points off top.
Rossiter joined the Gers in 2016 from Liverpool but was quickly hit by injuries which have stalled his career.
The prospect of linking up with former Gers team-mate Joey Barton at Fleetwood could also appeal.
Barton took the reins at Highbury in the summer so that could entice Rossiter back down south.
Gers midfielder Jason Holt is currently on loan with the Cod Army.
With tough competition for places at Ibrox, a move away in the short-term makes sense.
Playing regularly would allow Rossiter to re-establish himself before returning to Rangers.
There’s definitely a talented player there but injuries have meant we’ve seen very little of it.
A few months away and playing regularly could set him up to make his mark at Ibrox next season.
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