City are reported to have added Gomez to their shortlist but the final decision will come down to Pep Guardiola.
Gomez joined the Black Eagles on-loan at the start of the season and has hit the ground running scoring 21 times in all competitions for the Turkish league leaders.
The experienced striker became the first foreign Besiktas striker to score 19 times in his first season at the club.
The Germany international has also attracted interest from Manchester United who are reported to be keeping tabs.
Gomez is technically on loan at Besiktas but the club have a buy-out clause option that remains active until the end of the season.
The 30-year-old striker is reported to be happy at Besiktas but if he does return to Fiorentina and if the Italian club decide to sell him the Black Eagles will make 50 percent of the transfer fee according to the Sabah.
The Besikas star has even managed to return to the Germany national team having been called up for the last two round of matches and is expected to travel with the squad to the European Championship’s this summer.