United need a new back-up keeper to replace Martin Dubravka, who was recalled by Newcastle after spending the first half of the season on loan at Old Trafford.
Butland moved to Palace in 2020 but is behind established No1 Vincent Guaita and has also faced increased competition following the arrival of Sam Johnstone last summer.
A move to United would see the 29-year-old become understudy to David De Gea for the remainder of the season.
Butland, who was in the England squad at the 2018 World Cup, has not played for Palace this season. He made only two appearances last season and his last Premier League appearance was in May 2021.
United named 36-year-old Tom Heaton on the bench for their win over Bournemouth on Tuesday after Dubravka returned to Newcastle.
They have targeted Butland as he has Premier League experience, and hope a deal with Palace will be straightforward to agree.