The 20-year-old Germany international, who has a contract with Schalke until June 2019, has been in superb form in 2015-16 and his performances have not gone unnoticed across Europe.
Schalke have so far been adamant that they have no intention of selling Sane, but that has not stopped interested clubs from keeping a close eye on his situation at the Veltins Arena.
RB Leipzig previously made headlines when they signed Germany Under-21 striker Davie Selke from Werder Bremen and they are now dreaming of luring Sane to the Red Bull Arena as well as they aim to challenge Germany's finest.
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"Sane is an interesting option for us as well," RB Leipzig sporting director Ralf Rangnick told Sport Bild.
"I can imagine that his current contract situation could lead to interest from us. We already looked into signing him two years ago when he was not yet part of Schalke's first team.
"But if Europe's big clubs are indeed interested in signing him, his wages could prove to be too much of an obstacle. Plus the transfer fee that is being touted is above what we are willing to pay for a player.
"And it obviously remains to be seen whether he is interested in leaving Schalke. I have experienced first-hand that a lot of youngsters are Schalke through and through."
RB Leipzig sit top of the 2. Bundesliga table halfway through the season.