The 29-year-old scored 17 goals and provided four assists in 35 competitive matches last season.The attacking midfielder earned a place in Germany's World Cup squad, making two substitute appearances during the tournament.
Sky Sport Germany now reports that RB Leipzig want to sign Amiri ahead of the coming season. It is not yet clear how much Mainz would demand to let their star player leave.
Amiri is under contract with the club until the summer of 2028.
The midfielder has scored 26 goals and provided 13 assists in 82 competitive matches for Mainz since his move from Leverkusen. His form last season, particularly a goal return of 17 in all competitions, has clearly attracted attention from elsewhere in the Bundesliga.
Amiri began his senior career at Hoffenheim before moving to Leverkusen in the summer of 2019, spending four and a half seasons at the club before his switch to Mainz. His 17 goals in all competitions last season included a career-high 12 in the Bundesliga alone, a return that played a significant role in his recall to the Germany squad.
RB Leipzig are understood to view Amiri as a player capable of adding both goals and experience to their midfield.
Mainz, for their part, will be reluctant to lose one of their key attacking players, and any deal is likely to hinge on the fee RB Leipzig are willing to offer for a player who still has two years remaining on his contract.
Amiri's performances at the World Cup, however limited in minutes, will have done little to lower his valuation, with Leipzig facing competition from elsewhere in Germany's top flight should they move to formalise their interest in the coming weeks.
The midfielder's versatility, capable of playing both as a deeper playmaker and further forward, adds to his appeal for a Leipzig side looking to strengthen their attacking options ahead of the new campaign.