Zaha, 20, has been targetted by top Premier League clubs but United are on pole position despite offering lesser than Palace's valuation of the player.
Palace boss Ian Holloway wasn't ready to listen to offers less than £20 million but know clubs will not spend so much for a young winger.
United are currently in talks with Palace and are willing to send Zaha back on loan for the rest of the season along with other players to boost their promotion chances.
Zaha's transfer to Old Trafford could see Portuguese winger Nani heading out of Manchester Untied. The 26-year-old has been linked with Arsenal and Chelsea but none have made any concrete offer.
Meanwhile, Zaha already has five goals in 25 appearances in the Championship and also made his England debut as a substitute in England's 4-2 friendly defeat by Sweden.