Man United placed Fletcher in charge of the first-team squad following the sacking of Ruben Amorim on Monday.
The former midfielder will be in the dugout when the Old Trafford club take on Burnley later tonight, but talks for an interim manager to replace him afterwards are ongoing.
United have been linked with Ole Gunnar Solskjaer, Michael Carrick and Ruud van Nistelrooy. While they have held talks with them, Fletcher is also in the running.
He can enhance his chances of getting the interim role until the end of the campaign if he oversees an impressive victory and performance tonight.
It is unclear if Fletcher will remain in the dugout for the game against the Seagulls on Sunday, but he will be keen for a chance to prove himself.
All eyes will be on Fletcher and how the Red Devils play tonight, and the board will make a final decision regarding an interim boss in the coming days.
Man United will have plenty of options to choose from in the summer when it is time to pick a permanent manager.
They have reportedly identified Crystal Palace manager Oliver Glasner as a top candidate for the job at the end of the season.
The Austrian is out of contract at Selhurst Park this summer, and his achievements have impressed the Red Devils.