The report claims that Ospina would be able to leave the Gunners for £3 million but also states that the Colombian international has offers from other clubs as well.
The Black Eagles have already held initial talks with Ospina’s agent but have yet to submit an offer to the North London based outfit.
Ospina struggled for playing time last season following the signing of Petr Cech and is expected to leave over the summer.
Besiktas also made an offer for Ospina last season as well as in January but both times the deal fell through.
The Gunners may however, be keen on keeping Ospina on if on-loan keeper Wojciech Szczesny decided to stay at Roma on a permanent move.
Besiktas would be able to offer Ospina the guarantee of regular first-team and Champions League football next season if he were to make the move.
The Istanbul giants won the Turkish Super League title last season and booked a direct place int he Champions League group stage.