Sky Sports News is reporting that the Eagles have rejected a bid from Manchester United that would have risen to £50m.
The same article stats that the Red Devils offered an initial £35m as well as additional payments of £15m.
According to the same story, Crystal Palace were unhappy with the structure of the deal and the London side want between £45m and £50m up front.
Sky Sports News go on to add that the England Under-21 international is eager to secure a move to Manchester United.
However, the report adds that Wan-Bissaka, 21, has not attempted to force Crystal Palace’s hand by submitting a transfer request.
Manchester United manager Ole Gunnar Solskjaer is expected to overhaul the Red Devils squad in the current transfer window.
The 20-time English champions finished in sixth place in the Premier League table last term.
Manchester United have already signed Wales international Daniel James in a £15m deal from Championship side Swansea City earlier this month.
The Red Devils released Spanish midfielder Ander Herrera and Ecuador international Antonio Valencia earlier this summer.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news