Martin Dubravka moved to Old Trafford on loan from Newcastle United over the summer, but the experienced goalkeeper was recalled by the Magpies earlier this month.
As a result, Tom Heaton is the only senior replacement for David de Gea and the club are therefore looking to bring 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 transfer window and, according to journalist Guillermo Rai, a deal is now nearing completion.
Rai assures that the Red Devils have reached an agreement with Palace to sign the goalkeeper, who will undergo a medical with the 20-time English champion on Thursday.
The journalist claims it will be a loan deal until the end of the season, and it is unclear if Man United would consider signing him permanently this summer.
Butland has yet to feature for Palace during the 2022-23 campaign, although he was only back on the bench on Boxing Day as he missed the start of the season with a broken finger.
The goalkeeper was in the squad against Fulham and Bournemouth on December 26 and 31 respectively, but was not on the bench against Tottenham Hotspur on Wednesday night.
Butland only has a contract at Selhurst Park until the end of June, which means that, as it stands, he will be available on a free transfer at the end of the season.
The nine-time England international began his professional career with Birmingham City, making 46 appearances for the club before moving to Stoke City in 2013.
The most successful period of his Butland career came with the Potters, as he represented them on 168 occasions, which included 77 Premier League appearances.
The stopper joined Palace in 2020, but has been a backup during his time at Selhurst Park, making just 17 appearances for the Eagles in all competitions.
Butland will battle Heaton to be number two at Old Trafford for the rest of the season, and the goalkeeper could be in the squad against Charlton Athletic in the EFL Cup on Tuesday if a move is made in the coming days.
De Gea, who has entered the last six months of his contract with Man United, has once again expressed his desire to end his career with the 20-time English champions.