The 23-year-old was a reported target of the Scottish champions.
Earlier this month, sports publication Kicker noted interest from Rangers with the player’s deal at FC Köln expiring.
A versatile central midfielder, helped Germany win the Under-21 European Championships this year.
It was reported that a contract extension was unlikely. However, Köln now have a new manager in Steffen Baumgart and the club are keen to extend his deal.
According to Kicker, Özcan is close to signing a new deal with terms agreed.
Rangers, who are set to return to pre-season this week, have so far added striker Fashion Sakala to the squad after a pre-contract agreement, while Nnamdi Ofoborh joins from Bournemouth having agreed a deal at the start of the year.
The Ibrox side are not in competitive action until the start of the cinch Premiership season at the end of July.