Sky Italia reporter Gianluca Di Marzio also confirmed that the Istanbul based club are in talks with the Germany international.
The Independent recently stated that Liverpool are considering swapping Mario Balotelli with Mario Gomez.
Besiktas sold Demba Ba to Shanghai Shenhua for €14 million last month and are in the market for a replacement striker.
Ba joined the Eagles from Chelsea last summer and scored a career high 27 goals in all competitions in his debut season.
Gomez has a grand total of 166 goals in 308 appearances in all competitions throughout his professional career.