Wan-Bissaka has fallen out of favour at United under new manager Erik ten Hag and the club want to sign a new right-back before the transfer window shuts.
Borussia Dortmund’s Thomas Meunier has been mentioned as a possible target and his arrival would pave the way for Wan-Bissaka to leave.
Palace are keen to sign Wan-Bissaka this summer and have held preliminary talks over a possible move.
The Eagles sold the 24-year-old, who came through their academy, to Manchester United in 2019 for a deal worth £50million.
Any move now, however, would be considerably less than that and a fee of £10m has been mentioned.
United, however, could opt to loan Wan-Bissaka instead, in the hope he performs well this season and increases his value.
Big things were expected of the right-back when he moved to Manchester United, but he has struggled to perform since.
Wan-Bissaka lost his place in the first team last season, making just 20 Premier League appearances, and Diogo Dalot took his spot.
Dalot has been Ten Hag’s preferred option too since he was appointed and the Portugal international was a regular for United in pre-season.
The 23-year-old has started both of Manchester United’s first two Premier League games this season, playing the full 90 minutes, while Wan-Bissaka has been an unused substitute on both occasions.