Per the source, the Gunners are hopeful they can beat off interest from Borussia Dortmund and AC Milan.
Ozyakup left Arsenal four years ago after rising through the youth ranks and has established himself as one of the brightest talents in the Super Lig.
The 23-year-old contributed directly to 18 goals last season – 10 goals, 8 assists – playing a key role in the Black Eagles wining the league title and booking a place in the Champions League.
The former Arsenal youth is also a regular call up to the Turkish national team setup and has 23 international caps since making his debut in 2013.
The Gunners could however face stiff competition from Manchester United who the Daily Star report are willing to offer £20 million for his services after scouting the midfielder over the past 12 months.
Besiktas president Fikret Orman did not too long ago state that if Ozyakup were to leave he would not mind it being to United.
However, both Arsenal and United would have to probably wait another 12 months before they can sign Ozyakup – unless an offer too good to refuse is made.
Speaking at Adriano’s signing ceremony Orman revealed said: “Ozyakup was come a long way in four years, he is our stay player and will stay this season and experience Champions League football as a star player.
“It has been a great pleasure to see him develop and he will be here this season but once his mission at Besiktas is complete he can decide his future.
“I would love him to stay here until he retires but we will discuss his future next season.”