The 21-year-old made the second highest number of tackles (90) and interceptions (84) in the entire English top flight this season, and is now on worldwide duty with the England U21 side.
Although initially starting out as a squad player, the England U21 global became a regular starter for the Premier League side in the 2018-19 season, making 39 appearances in all competitions.
Palace believe they are in a strong position after securing Wan-Bissaka on a contract until 2022, and the 21-year-old has said he is happy to stay at Selhurst Park next season.
James is Man United-bound as Solksjaer begins overhaul
He is on global duty with Wales and started for Ryan Giggs' side on Saturday away against World Cup finalists Croatia . James spent seven years at Hull's academy before leaving for Swansea as a 16-year-old in the summer of 2014.
The Mancunian giants have been looking for a new first-choice right-back ever since the management decided not to offer former club captain Antonio Valencia a new contract. They will have to fight with Crystal Palace however, who desperately need to keep the Englishman if they want to keep their defense together.
"I think you spend £30m-£40m and then try to improve them, which will also give you longevity out of the players and allow you to build a squad around the five or six new players that come in, plus a few of the players who are still there".
Wan-Bissaka made three assists in 35 games in the Premier League in the 2018-19 season.