The Jamaica boss is in no doubt that the Turkey teenager can go on to emulate the Arsenal playmaker - provided he gets the right support from Bert van Marwijk at the Imtech Arena
The 19-year-old attacking midfielder is considered one of the most exciting young talents in the Bundesliga and has already been capped at international level by Turkey.
Calhanoglu made his professional breakthrough at Karlsruher and even returned to Wildparkstadion on loan last season, helping the club win promotion to 2. Bundesliga, and Schafer is in no doubt that the youngster has what it takes to establish himself as one of the best players in the world.
"Calhanoglu is the new Ozil," the Jamaica boss told Bild. "Hakan is an exceptional boy. He has a lot of confidence and courage. He is simply great."
However, Schafer believes that Hamburg coach Bert van Marwijk will have an important role to play in whether Calhanoglu realises his full potential.
"Like Mesut, he can go right to the top," the 63-year-old insisted. "But for that he needs a coach who will try every day to make him better. Hakan needs a coach who will always encourage and support him mentally.
"I do not know how Bert van Marwijk operates but I hope he takes to Hakan. If not, Hakan has to go another club where he can take the next step up."