The 29-year-old’s future at La Viola is not secure with new coach Paulo Sousa not keen on keeping the German forward at the Stadio Franchi.
Meanwhile, Liverpool are looking to increase their attacking options with speculation linking Mario Balotelli, Fabio Borini and Rickie Lambert with the Anfield exit door.
According to La Nazione, Gomez is reluctant to leave Fiorentina, but would be willing to listen to any offer presented by Liverpool who are thought to be keen to bring the player to the Premier League.
Gomez has endured an injury hit period with Fiorentina since moving to the club from Bayern Munich in 2013, and scored just four goals in 20 Serie A appearances last season.
Elsewhere, Napoli striker Gonzalo Higuain wants his club to consider offers from Liverpool this summer.