In his most recent press conference Ospina stated: “Arsenal want a lot for him [Ospina] so we may have to look for alternatives.”
Orman did however, confirm that he would like to see the Colombian keeper at Besiktas next season.
“I do want Ospina and we are going to get a foreign keeper,” he added.
Ospina has played a key role for Colombia in the Copa America and is set to start against Chile in the semi-finals at Soldier Field, Chicago, Illinois.
The 27-year-old still has another two-years remaining on his contract but has hinted that he will leave Arsenal over the summer as he wants regular first team football.
Ospina would be almost certain to establish himself as first-choice keeper at Besiktas and the Super Lig title holders would be able to offer Champions League football.
The Colombian keeper made 14 appearances for the Gunners last season keeping four clean sheets over the course of the season conceding a total of 17 goals.