The pair played together at Schalke before Sane left for Manchester City.
Schroter recalled to BILD: "It was very, very clear that he was a very special player. I always expected it, that he makes the breakthrough. But I did not expect him to shoot through the ceiling in such a short time. He has developed in all respects.
"If you train under a coach like Pep Guardiola, that almost happens automatically.
"In the past he might not always have the focus and was a bit distracted in Schalke at times. Under Guardiola he has now developed the greed to want to get better and better. His passing game, his moves towards the goal - now everything is much more purposeful with him."