Mateta, 23, is keen to leave the Bundesliga side and Palace have submitted a bid for him.
RMC Sport reveals that Palace’s first offer was refused by Mainz, but that negotiations continue for the highly-rated Frenchman.
Meanwhile, BILD states that Palace are willing to pay €15m for Mateta, who has scored 17 goals in 54 games for Mainz.
The German publication adds that Mateta will either be a backup or replacement for Christian Benteke if he joins Palace.
However, Palace are not the only Premier League club interested in Mateta and other offers could arrive.