Black Eagles president Fikret Orman sparked further speculation when he liked four pictures from Falcao’s official Instagram account.
Former sporting director Sinan Engin revealed live on Beyaz TV that Besiktas are lining up the Colombia international as a replacement for Mario Gomez in the event that he leaves over the summer.
The experinced striker 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.
Falcao joined Chelsea on loan but struggled to settle in scoring just one goal in 12 appearances for the reigning champions this season.