Town and the Premier League Saints are waiting to discover from the FA's Professional Game Board whether last Saturday's postponed third round tie will take place at a later date after a big Covid-19 breakout at Shrewsbury.
And, if the St Mary's clash does go ahead, the reward will be a contest against Mikel Arteta's Gunners, who are 11th in the top flight. Arsenal are record winners of the competition, with 14.
The draw for the fifth round of the competition also took place tonight and sees Shrewsbury, Southampton or Arsenal head to the winners of National League North Chorley and Premier League Wolves.
That fifth round tie at Chorley or Wolves will take place on Wednesday, February 10.
Reports this evening suggest the Premier League are keen to reach a conclusion where Shrewsbury do not have to forfeit their place in the competition after being unable to fulfil the tie last weekend.
One suggestion is that Southampton's top flight clash against Leeds at Elland Road next Wednesday (January 20) could be postponed in order to fill in the Shrewsbury tie. It is understood the Premier League are considering this option.
That would come before the fourth round weekend, which is scheduled for January 23.
With a tie against Arsenal – who are in action in every midweek until the fifth round next month – at stake, it looks likely that the only chance Shrewsbury have to fit their third round tie in would be next Wednesday, when Southampton were set to travel to Leeds.
But with Town Sundorne Castle training facility shut until Friday at the earliest, it would still represent a tight turnaround for players to train and return to fitness for the clash having not played for more than three weeks.
It would also require Shrewsbury's significant number of players and staff to have tested positive to return a negative test, in order for training to resume.