The youngster has come on leaps and bounds in the past season at Palace.
The 20-year-old is seen as one of the best young full backs in the league, with Everton not the only team interested.
The Daily Mail claim the Toffees see Wan-Bissaka as the long term replacement for Seamus Coleman.
And they are prepared to offer Ademola Lookman in a part-exchange for Bissaka.
The English fullback has a contract at Palace until 2020.