Ospina is expected to hold direct talks with Fenerbahçe after Colombia crashed out of the Copa America on penalties against Argentina.
The Colombian international keeper recently stated that he was completely focused on the South American football tournament and that he would not be talking about transfers while in Chile.
Ospina did however, ask reporters to talk to his agent regarding interest from Fenerbahçe.
The 26-year-old keeper is expected to leave the Gunners over the summer following the arrival of Petr Cech.
Ospina is expected to fall down the pecking order behind Cech and Wojciech Szczesny despite playing as the Gunners first choice keeper for much of the second half of the season.
The Independent reports that despite Ospina being the more likely to leave he made just 0.06 errors per game that led to goals compared Szczesny who made 0.18.
The Colombian international also averaged more saves per-match 1.94 to 1.65 and kept a total of 10 clean sheets last season.