Black Eagles president Fikret Orman sparked further speculation when he liked four pictures from Falcao’s official Instagram account.
The Germany international has been in fantastic form for the Black Eagles scoring 27 times this season for the league leaders but he is on-loan and Besiktas have yet to activate his release clause.
Gomez has 25 goals in the league but has attracted the interest of several Premier League and Bundesliga sides.
Besiktas have underlined that their priority is to keep Gomez at the club but that they will plan for all possibilities.
Chelsea striker Radamel Falcao has revealed that he is returning to Monaco next season after being told he is no longer needed by the Blues.
Falcao joined Chelsea on loan but struggled to settle in scoring just one goal in 12 appearances for the reigning champions this season.
The Colombian international’s injury-plagued season is his second consecutive poor campaign in the Premier League. Falcao scored just four times in 29 appearances for Manchester United in the 2014-15 season.