The Turkish transfer window doesn't close until Friday and Besiktas have become the leading club for Frei's signature.
"We are in the process of trying to sign Kerim Frei from Fulham," Orman told Lig Tv.
"If Fulham accept our terms, the deal will be done quickly.
"We have been in contact with him for a long time."
Besiktas are ready to offer £2m for the 19-year-old, according to The Metro.