The report claims that the Black Eagles are keen on signing Ospina who is expected to leave Arsenal over the summer after growing frustrated with his lack of playing time at the club.
Ospina recently was recently quoted in the Evening Standard as saying: “It’s hard, because as a player, you always want to play,” he said.
“If you don’t play you have to give your best in training and make sure you train to the highest possible level in order to ensure that you are ready whenever the manager calls on you.”
The Gunners are reported to be prepared to part ways with Ospina over the summer as Arsene Wenger plans his overhaul of the squad.
Besiktas did sign Denis Boyko over the winter transfer window after failing to buy Ospina in January but have not been pleased with his display so far.
The Istanbul giants would prefer Ospina going into the Champions League next season after winning the league title.
Besiktas conceded the most goals in the top three despite winning the league and Senol Gunes has made it his priority to bolster his goalkeeping and defensive positions.