Orman did however, state that the Gunners will have to lower their asking price for the Colombian international.
“We are going to get a foreign keeper. I do want Ospina but Arsenal want a lot for him so we may have to look for alternatives,” Orman said in his press conference.
Ospina is currently on intentional duty with the Colombia national team for the Copa America and will take on Chile in the semi-final at Soldier Field, Chicago, Illinois.
The 25-year-old keeper is expected to leave Arsenal after the tournament in pursuit of first team football.
Besiktas would be able to offer first team and Champions League football on a lucrative contract if he were to make the move and has been a target of the Istanbul giants for the past season.
The Black Eagles also made an offer for Ospina in January but the deal fell through.
Besiktas won the Turkish league title last season but had the worst defensive record in the top three and have made strengthening at the back a priority over the summer.