Sane, 29, is yet to put pen to paper on a new deal at Bayern Munich, with his current contract due to expire at the end of the season.
According to Sky Deutschland, Arsenal have already entered talks with Sane’s representatives over a move to the Emirates.
Kane, 31, has weighed in on the situation, admitted that he wants Sane to remain at the club beyond the summer.
The England captain told Bild: "It's obvious that I harmonize very well with him. He has great qualities and terrifying skills.
“It was a top game from him (against St. Pauli) and great to see how he converted his chances. He often gets into those positions and was ice-cold in front of goal, which is what we need."
He added: "It's not my decision, but the club's. I really like playing with Leroy and would love for him to stay. But that's a discussion between him and the club."