Martin Dubravka moved to Old Trafford on loan from Newcastle United over the summer, but the experienced goalkeeper was recalled by the Magpies at the start of this month.
As a result, Tom Heaton is the only senior back-up to David de Gea, and the club are therefore looking to bring in another stopper during the January transfer window.
On Wednesday, it was reported that Man United had identified Butland as the ideal acquisition during the winter market, and according to journalist Guillermo Rai, a deal is now on the verge of being completed.
Rai claims that the Red Devils have come to an agreement with Palace over a move for the goalkeeper, who will undergo a medical with the 20-time English champions on Thursday.
The journalist claims that it will be a loan deal until the end of the season, and it is unclear whether Man United would consider signing him permanently this summer.
Butland is yet to make an appearance for Palace during the 2022-23 campaign, although he was only back on the bench on Boxing Day, having missed the start of the season with a fractured finger.
The stopper was in the squad against Fulham and Bournemouth on December 26 and December 31 respectively, but he was not on the bench against Tottenham Hotspur on Wednesday night.
Butland only has a contract at Selhurst Park until the end of June, meaning that, as it stands, he will be available on a free transfer at the end of the season.
The nine-time England international started his professional career with Birmingham City, making 46 appearances for the club ahead of a switch to Stoke City in 2013.
Butland's most successful period of his career came with the Potters, as he represented them on 168 occasions, which included 77 appearances in the Premier League.
The stopper joined Palace in 2020, but he has been a back-up during his time at Selhurst Park, only featuring on 17 appearances for the Eagles in all competitions.
Butland will battle Heaton to be the number two at Old Trafford for the remainder of the season, with the goalkeeper potentially being in the squad against Charlton Athletic in the EFL Cup on Tuesday if a move goes through over the next couple of days.
De Gea, who has entered the final six months of his contract at Man United, has again expressed a desire to finish his career with the 20-time English champions.