The Guardian says Palace could use United's push for Wan-Bissaka to remove a sell-on clause from Zaha's transfer deal.
The Eagles re-signed Zaha permanently from United back in 2015, with the Red Devils demanding a percentage of any fee received in any future sale as part of the arrangement.
Zaha looks to be on the move this summer, after telling Palace he wants to leave the club.
It is thought that Palace could command up to £80 million for the Ivorian, but a significant chunk of that would go to United under the current conditions.
Palace are now hopeful of removing the clause in Zaha's contract as part of any deal that takes Wan-Bissaka to Old Trafford.