Szalai, 25, has been in scintillating form this season, netting 9 times in 17 Bundesliga appearances.
As a result, the player, who spent three years at Real Madrid before joining Mainz, is now followed by Arsenal, Borussia Dortmund and Wolfsburg.
The Bundesliga club are desperate to keep hold of their star player, and general manager Christian Heidel claims there has been no contact with interested sides.
“There is nothing concrete. We will not sell him now for any amount of money,” Heider was quoted as saying in Bild.
However, it appears Mainz might not be able to resist a big money offer next summer.
“If someone comes to us with a €20 million offer…”
Adam Szalai began his professional career at Stuttgart, but left the Swabians for Real Madrid in the summer of 2007.
The Hungarian joined Mainz after failing to make a single senior appearance for los Blancos, and has since scored 17 goals in 67 Bundesliga matches.