The Argentinian winger joined Metalist on a four-year contract from Catania in the summer, but has struggled to settle in the Ukraine.
The 25-year-old was linked with Fiorentina before he signed for Metalist, with Inter Milan and Atletico Madrid also rumoured to have been interested.
Gomez has acknowledged he made a mistake in accepting Metalist's offer and he is hoping that the club will allow him to return to Serie A in the January transfer window.
"I want to play in Italy," Gomez told tuttomercatoweb.com. "I'd like to go, in particular, to Fiorentina, where I was going to go two years ago.
"Here, it's cold, the language is difficult to understand. The team is good, but the rest is bad. I have failed to settle, I'm not happy.
"Metalist's offer was advantageous, but I was wrong. I would like to move in January if there was the possibility, at the latest in June.
"The Ukrainian league has little visibility and I don't want to waste any more time.
"I have already said to Metalist I want to go. I am ready to cut my salary in order to return to a high-level championship like Italy."