The La Liga giants have submitted for the Turkish international star but have not matched the Black Eagles £20 million asking price.
Ozyakup has seen his value increase a whopping 2700 percent from just £425K in 2012 to £11.9m in 2016.
United sent scouts to keep tabs on Ozyakup in his opening game of the season according a source close to the club told Turkish-football.com.
The 23-year-old put on an impressive display in the Eagles 4-0 victory against Alanyaspor.
Ozyakup will be competing in the Champions League this season after playing a key role in Besiktas winning the league title scoring 10 times and providing eight assists in the process.
The creative midfielder is no stranger to the Premier League having rose through the ranks at Arsenal before joining Besiktas in 2012 in pursuit of first-team football.