The Turkish sports newspaper claim that Dortmund have been keeping close tabs on the former Arsenal youngster.
Dortmund boss Thomas Tuchel is reported to have ordered scouts to continue watching Özyakup after being impressed with his recent performances.
Arsenal have been preparing a £9.3 million bid for former youth academy player Oğuzhan Özyakup according to the Milliyet.
The Turkish international star spent four years at the Arsenal academy and played a key role in the Under-18s side that won the Premier Academy League title in 2009 before joining Beşiktaş on a £500,000 move in 2012.
Özyakup is currently the fourth highest rated player statistically according to Whoscored and the best ranked Beşiktaş player with a 7.54 score.
The 23-year-old averages the highest number of key-passes per-game (2.9) in the league and an average of 60 passes at an 84 percent success rate.