United have been scouting the French striker this season - including in last week's FA Cup win for Palace against Millwall. Mateta's time on the pitch was cut short after an ugly collision with Lions goalkeeper Liam Roberts, which left him eventually needing 25 stitches to a head wound.
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Palace boss Oliver Glasner has stated Mateta will play again by the end of the month.
Meanwhile, L'Equipe says United have now opened talks with Palace over a deal for Mateta.
Mateta's contract at Selhurst Park runs to 2027, leaving them under no immediate pressure to sell. However, the Eagles would be willing to cash in at a starting price of £40m.
For his part, the striker feels ready to leave Palace for a bigger stage.