The Dutch-born midfielder is highly-rated and has made 163 appearances since joining Besiktas from Arsenal in 2012. He has scored 24 goals in that time.
According to Fotospor, the London club are also understood to hold a contractual clause from that deal which entitles them to '30% of next sale' for Ozyakup.
In principle, that means Arsenal could be due as much as €5m from the reported transfer deal.
Ozyakup is highly-rated in Turkey and Europe, being described as an energetic and attacking-minded central midfielder. Lazio reportedly made an offer for the player in 2016.
He has made a total of 24 league appearances for Besiktas this season, creating four assists for his teammates, as well as playing in the Champions League.
Former Turkish international footballer Ridvan Dilmer called Ozyakup a "magician" and has described his dribbling abilities as "Zinedine Zidane-like" in the past. He has also been lauded for his leadership qualities by former international players.
Ozyakup represented the Netherlands at U17 and U19 levels, but switched allegiances to Turkey at U21 level. The 25-year-old has since made 30 senior appearances for Turkey, scoring his only international goal against the country of his birth in 2015.
Should a deal for Ozyakup materialise, he would become Newcastle's second transfer of the summer window, having already made the permanent signings of on-loan Slovakian goalkeeper Martin Dubravka.
Manager Rafa Benitez is understood to have a wealth of targets in mind for every position in the Newcastle team, and - as seen with the likes of Dubravka - his scouts are more than capable of finding quality talent in less well-scouted areas of the continent.