The 21-year-old has made just 42 Premier League appearances for the Eagles, but was an outstanding performer last season.
An initial fee of £45 million with an extra £5 million in add-ons has reportedly been agreed between the clubs, according to the reports.
That fee would make Wan-Bissaka the most expensive defender in United’s history.
The Red Devils are in need of an overhaul after finishing sixth in the Premier League last season to miss out on Champions League qualification.
A long-term replacement at right-back for club captain Antonio Valencia, who left Old Trafford at the end of last season when his contract expired, was one of Ole Gunnar Solskjaer’s priorities in the transfer market.
Wan-Bissaka will become United’s second signing of the summer following the arrival of winger Daniel James from Swansea as United turn their attention towards young, British players rather than the expensive star buys of recent seasons.
The England under-21 international is expected to travel to Manchester for a medical on Wednesday after a disappointing under-21 European Championships in Italy.
Wan-Bissaka scored an injury time own goal to gift France a 2-1 victory in England’s opening game and was then dropped for matches with Romania and Croatia as Aidy Boothroyd’s side crashed out at the group stages.
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