United have been scouting the Frenchman this season and opened a first round of talks with Palace last week about a summer transfer.
The Mirror says Palace are prepared to do business for £40m - almost half of what Sporting CP are seeking for Viktor Gyokeres.
The Swede is United manager Ruben Amorim's preferred option for a new centre-forward signing, but the board are insisting there is no money for such an addition.
Indeed, even meeting Mateta's price will require United needing to sell to fund the deal.
Mateta is currently recovering from an ugly collision with Millwall goalkeeper Liam Roberts a fortnight ago, which required 25 stitches in a head wound. However, Palace are hopeful of the striker making their FA Cup quarterfinal against Fulham at the end of the month.