The 28-year-old joined the Grifone on a four-year deal from Belgian side Genk last summer, but struggled for consistency in his first season in Italy.
Sky Sports News reports that Gianfranco Zola is considering a move for the Hungarian international, who admitted to difficulties last year.
"I'm a Genoa player, so this is the only sure thing," Tozser told Nemzeti Sport.
"I wasn't satisfied with my latest season, but it's not because of the time I spent on the pitch.
"About the difficulties at Genoa, I would say it can be a negative thing when players keep coming and going from the club."
Tozser has won 20 caps for his country.