The Black Eagles are reported to be closing in on a deal for the Germany international.
Fanatik claim that Fiorentina do not want to pay the experienced striker’s wages. Gomez makes €5.5 million per-season and still has another year left on his current deal.
Liverpool are also reported to be in the race for the 30-year-old striker and his agent Uli Ferber has revealed that he has been in talks with clubs other than Beşiktaş.
Ferber told German magazine Sport1: “There are negotiations going on with several different clubs, including Besiktas.
“But nothing has been signed or agreed on yet. Nothing is decided.”
Beşiktaş are in the market for a new striker after selling Demba Ba to Chinese giants Shanghai Shenhua for €14 million last month.
The Black Eagles finished last season in third-place and booked a place in the Europa League group stages.
The Istanbul giants recently completed the transfer of Porto winger Ricardo Quaresma and are also expected to sign Brazilian defender Rhodolfo.