The Black Eagles have already lost Gokhan Tore on loan to West Ham and last seasons top scorer Mario Gomez will not return over the summer.
The Istanbul giants want to keep hold of their remaining key players going into the Champions League campaign.
Besiktas are under the watch of FFP and value Ozykaup as being worth £20 million. In the event of their valuation being met the Eagles would face a tough decision however, the club held a meeting with the 23-year-old discussing the current situation and he is happy to stay at the club for another season.
Besiktas President Fikret Orman has made no secret that the club do plan to sell Ozyakup for a profit in the near future and even stated that he would like to see the 23-year-old join the Red Devils.
Ozyakup is no stranger to English football having played for Arsenal as a youth player before joining Besiktas for £350,000 in 2012.