The 26-year-old has already expressed his desire to leave Palace this summer, in search of European football next season.
Yesterday, Arsenal submitted a £40million bid plus add-ons for Zaha, but Palace are demanding £70m.
Although there is a possibility of a return to Old Trafford, the Ivorian is keen to sign for the Gunners, who he supported as a young boy.
Also, Zaha wants to stay in London for family reasons.
Zaha endured a difficult spell at Man United during the 2013/2014 campaign, before returning to Crystal Palace, where he signed a new five-year contract last year.