Off contract this summer, Sane is primed to leave Bayern Munich after signing with Zahavi this month.
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His decision to leave long-time agents 11Wins for Zahavi has coincided with him rejecting Bayern's new contract offer.
Sky Deutschland says Zahavi is now in contact with Levy about the prospect of a free transfer to Spurs.
Spurs' Champions League qualification, through winning the Europa League last week, is a key factor in Sane's thinking.
A move to London would represent a return to the Premier League for Sane, who is a former Manchester City player.