The German international, who was a reported target for Liverpool, joined Fiorentina in 2013 from Bayern Munich.
He now looks set to move to Istanbul and replace Senegalese hitman Demba Ba, who left Besiktas this summer to join Shanghai Shenhua.
“Talks over the transfer of Mario Gomez have been opened with the player and his club,” Besiktas said in a short statement.
Gomez, 30, has won 60 caps for Germany in an illustrious career, although he missed Germany’s 2014 World Cup triumph due to injury.
If the signing is completed, Gomez will be the latest big-name player to be joining the Turkish Super Lig ahead of next season for one of the big three Istanbul sides.
His compatriot Lukas Podolski has joined reigning champions Galatasaray while Dutchman Robin van Persie and Portugal’s Nani both signed for 19-time winners Fenerbahce from Manchester United.