Having so far only brought in Daniel James from Swansea, Ole Gunnar Solskjaer's side are looking to kick-start their summer rebuild by signing the talented 21-year-old right-back.
It’s understood that talks between United and Palace continue after Wan-Bissaka returned from the Under-21 European Championship following England's group stage exit.
There is a belief within Old Trafford that a deal can be struck with Palace for their academy graduate, and the club is hopeful of having Wan-Bissaka on board in time for the start pre-season on 1 July.
Leicester defender Harry Maguire is another player interesting United as they look to improve in central defence, while Press Association Sport understands that Sporting's Bruno Fernandes is among the rated midfielders.
The Portugal international enjoyed an outstanding season at the Lisbon club, where a number of players are due to return to pre-season on Wednesday.
Fernandes, though, is currently on holiday in Dubai after helping his country win the Nations League. Newcastle man Sean Longstaff is another player on United's radar.
Ander Herrera's exit has left United with a hole in midfield, while Paul Pogba is keen to get a "new challenge somewhere else" if possible - something which currently looks unlikely.
Romelu Lukaku is another big-name player open to an exit, but Press Association Sport understands that Inter Milan have yet to make a serious offer.
Questions also remain over the future of the likes of Alexis Sanchez, Marcos Rojo and Matteo Darmian.
Meanwhile, Real Zaragoza have denied reports that youngster Mateo Mejia has left the club for United.
A statement from the Spanish club read: "Real Zaragoza has not reached any agreement for the transfer of this player to Manchester United."
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