According to Sky Sport, the 19-year-old underwent his medical with Eagles as he is closing in on completing a season-long loan move to Selhurst Park. He will play under his compatriot Frank de Boer at Palace.
Fosu-Mensah is a versatile player, who can play anywhere in the back four, including both the full-back positions and also as a defensive midfielder. Jose Mourinho signed central defender Victor Lindelof and midfielder Nemanja Matic this summer.
The arrival of the Swedish international and the Serbian midfielder from Chelsea has seen Fosu-Mensah, drop further down the pecking order at Old Trafford. The Portuguese tactician has given a green signal in sanctioning the Dutchman's sale to the Eagles.
He arrived at United's academy from Ajax in 2014 when Louis van Gaal was the manager at the club. Fosu-Mensah made his first team debut against Arsenal in February 2016, under the guidance of the former Barcelona and Bayern Munich manager.
Under Mourinho, the former Ajax academy player made 11 appearances across all competitions, which included four starts. He was an unused substitute in United's 2-0 win over Ajax in the Europa League final in May and was also included in the Red Devils' pre-season squad for the United States this summer.
Fosu-Mensah's addition to De Boer's squad for the 2017/18 season is likely to improve their defence. Palace have so far signed Jairo Riedewald, another former Ajax academy graduate, this summer.
His current deal at United will run down in 2020. The teenager has admitted that he was not frustrated with the lack of first team opportunities under Mourinho's guidance the last term.
"It's fine because you're surrounded by great players. Every day, in and out, you train with great players. You develop every day with these great players," Fosu-Mensah told Press Association Sport, as quoted by the Daily Mail.
"I just want to develop, keep developing. I am young so I try to work on my weaker stuff and to become a better and complete player. I need a bit of experience, things like concentration, touches, communicating on the pitch."