According to BILD, Mainz will listen to suitable offers for Mateta, 23, and have put a €15m valuation on him.
They have made a formal inquiry for Mateta, although no official bid has been made yet.
Brugge are in next season’s Champions League, but Mainz are hoping that wealthy clubs – from England for example – join the race.
Since arriving from Lyon two years ago in a club-record €10m deal, Mateta has scored 17 goals in 54 appearances for Mainz.
The Paris-born attacker represented France all the way up to under-21 level.