The striker could return to a club where he enjoyed one of the best seasons of his career, having scored 28 goals in 41 games at Besiktas in the 2015-16 campaign.
The Turkish side's interest in the Stuttgart attacker was reported by 'beIN Sports', with Besiktas apparently seeing Gómez as the man to lead their attack in the coming seasons.
Despite now being in his thirties, Mario Gómez is still a player who knows where the goal is, scoring 8 times for a struggling Stuttgart side last season.
The former Germany international is out of contract in summer 2020, but Stuttgart's relegation to the second tier could mean that Besiktas pick up their former player for a much reduced price.