The Black Eagles have been closely linked with a move for the Colombian international but a club official had yet to confirm interest.
Keskin told Turkish radio station Radyospor: “Nothing has been agreed on yet but we are targeting Ospina.”
Ospina is currently preparing with the Colombian national team for the Copa America tournament set to be played this summer.
Turkish sports newspaper Fanatik claims that Besiktas are close to agreeing upon on a €3.5 million deal.
Meanwhile the Daily Star report that the Istanbul giants are preparing a £3 million bid for Ospina.
Ospina is currently behind Petr Cech in the Arsenal goalkeeping pecking order and is reported to be unhappy with his limited role in the squad.
Turkish Super Lig champions Besiktas would be able to guarantee Ospina first-team and Champions League football next season.