The move would serve to provide Montella with additional attacking depth, which, along with defensive reinforcements, is thought to be a priority this transfer market.
According to Sky Sport Italia, however, the Orobici are not prepared to let the 28 years old winger go.
Gomez, who has come back to Serie A football after a negative experience with Ukrainian club Metalist Kharkiv, has already worked with Montella during their shared time at former Serie A side Catania.
Since returning to Italy, Gomez has caught a lot of attention for his performances, having struck up a good relationship with compatriot Maxi Moralez, before the latter left La Dea last season.
Gomez showed a good form during his last season with the Nerazzurri, accumulating 34 Serie A appearances, while scoring seven goals and delivering nine assists in the process.