The German, 25, has had an inconsistent start to life with the Turkish side after signing a two-year loan agreement.
He was made surplus to requirements at Anfield following a series of blunders, and reports have suggested he could even be sent back to Merseyside after a mixed start in the Süper Lig.
But Besiktas chief Orman has brushed off that claim - and insists they want to sign up Karius for good.
"Karius is an excellent keeper, God willing we will sign him on a permanent transfer," he told Besiktas's club channel BJK TV .
"These stories are complete nonsense. Give Karius some time is all I'm saying. Karius has a lot of work to do but give him time."
Karius’ agent Florian Goll recently rubbished reports his client's time in Turkey could be cut short, saying: "Loris is on loan to Besiktas for two years - that's the situation.
"The club has no intention of ending this loan contract prematurely."