It is understood the bid was worth an initial £35m, with additional payments totalling to £15m.
Palace are understood not to be happy with the structure of the proposed deal, but it is believed they would accept £50m up front for the England U21 international.
Although Wan-Bissaka favours a move to Old Trafford, he has not put in a transfer request or agitated for the switch.
Palace are under no pressure to sell the 21-year-old, who featured 39 times in all competitions last season as the Eagles finished in 12th place.
Wan-Bissaka has three years remaining on his contract at Selhurst Park.
United manager Ole Gunnar Solskjaer is keen to bring in a right-back this summer following the departure of club captain Antonio Valencia.