The 24-year-old is set to end his 15-year stay at Koln and is on the verge of leaving the German club this summer.
West Ham have been interested in putting him at the disposal of David Moyes, while Bundesliga giants RB Leipzig have also been on his trail ahead of the transfer window.
But it has been claimed Dortmund are set to beat the competition to the signature of the midfielder in the coming days.
According to German daily Bild, Ozcan is currently being put through his paces at Dortmund for his medical.
An agreement is in place between Koln and Dortmund for the midfielder to move to the Westfalenstadion.
Koln are set to bag a fee of €10m for a player who could have walked away on a free transfer next year.
Personal terms have also been agreed upon between Ozcan and Dortmund and the completion of the transfer is now a matter of time.