Red Devils boss Jose Mourinho, who appears to have fallen out with Martial, has made the Blues winger his top target this summer.
And the Sunday Mirror believes that a potential swap deal could be on the cards, with both players valued at £75m and keen on a move.
Willian, 29, has been the subject of three Barcelona bids this summer and United are desperate to beat the Catalans to his signature.
The Brazilian returned to Chelsea training later than expected, citing passport issues as the reason, although Mautizii Sarri expects Willian to stay.
Martial, 22, struggled for starts under Mourinho last season and irritated the United boss by leaving their pre-season tour to witness the birth of his child.
