The Colombia stopper has been used sparingly following the arrival of Petr Cech at the Emirates.
The Colombia international goalkeeper has been reduced to a back-up role due to the arrival of former Chelsea No. 1 Petr Cech last summer in a £10 million deal.
Ospina took over from Wojciech Szczesny after manager Arsene Wenger lost his patience with the Pole for his blunders.
He was also caught smoking in the showers, as reported by the Daily Mail, following a FA Cup game with Southampton - a match which saw another individual mistake from the international keeper.
Stocky 27-year-old Ospina performed well between the sticks for the Gunners but was never able to cement his position after the arrival of the towering Czech. He has featured in just four league matches this term.
According to the Mirror, Turkey’s Besiktas are interested in Ospina, while Everton have also voiced their admiration duo to the impending departure of Tim Howard. However, any move to Merseyside may hinge on the future of under-pressure Toffees boss Roberto Martinez.