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It is believed Palace would be willing to pay £10m for the England international.
That figure would represent an embarrassing loss for United, who forked out £50m to sign the defender from Palace in 2019.
The report claims Wan-Bissaka is not part of United manager Erik ten Hag's plans for the season and will be allowed to leave this summer.
If a permanent deal is unable to be agreed with Palace, another option would be to loan Wan-Bissaka back to his former club in an effort to relaunch his career.
Ten Hag has informed United he wants the club to sign another right-back to provide competition to Diogo Dalot, should Wan-Bissaka leave.
United are said to have identified Meunier as a possible replacement for Wan-Bissaka, with a fee of around €15m (£12.6m) proposed for the Belgium international.
Meunier, 30, joined Dortmund on a free transfer from Paris Saint-Germain in 2020 and is currently under contract with the German club until 2024.
United are yet to make an official bid for Meunier, with Barcelona full-back Sergino Dest also on their list of targets.
Ten Hag is hoping to bring in several new signings before the transfer window closes.
United are keen to sign Real Madrid midfielder Casemiro and are reportedly prepared to pay as much as £67m for the Brazilian.
United's bid to sign Casemiro comes after failed attempts to entice Barcelona's Frenkie de Jong and Juventus' Adrien Rabiot to Old Trafford.
United are also keen to sign Christian Pulisic on loan from Chelsea, while the Red Devils have also been linked with a move for Barcelona forward Pierre Emerick-Aubameyang as Ten Hag looks to bolster his attacking options following consecutive defeats to Brighton and Brentford at the start of the new Premier League season.