The former England Under-21 international wants to move on to get his career back on track just 18 months after Sir Alex Ferguson paid £20m for him.
Zaha failed to impress David Moyes while the Scot was at the Old Trafford helm last season, and was loaned to Cardiff City.
Now the player is thought to be willing to cut his losses in the North West and is hoping for a move back to the capital, according to The Express.
Palace may test the water with a loan offer, but United are said to want a permanent deal and could accept a cut price £10m.
Sports Mole recently picked out Zaha as one of three players that Crystal Palace should sign.