The game, which was scheduled to be played this past Saturday, was postponed after a COVID-19 outbreak at Shrewsbury, affecting both players and coaching staff.
The Telegraph reported that Shrewsbury face being thrown out of the FA Cup if they can’t find a way to complete their fixture with Southampton and one way to do that is to see Saints’ Premier League clash at Elland Road pushed back.
At the time of writing, Southampton is set to take on Leeds on 20 January.
Talks between Saints and Leeds have apparently started already at the possibility of that game being postponed.
Leeds did take part in their third-round FA Cup fixture on the weekend. They lost to League Two side Crawley Town in a 3-0 routing.
If the fixture between Southampton and Shrewsbury is fulfilled, the victors will face FA Cup holders Arsenal in the fourth round.