The 20-year-old is one of the highest-rated prospects in Europe currently.
The Sun claims that the Bundesliga side were initially thought to have set a £40m asking price for the prospect, but it appears that any interested club will be able to do a considerably cheaper deal if they wait a few months before making a move.
The winger - who is also attracting the interest of Manchester United (via The Sun) - has been fantastic for his current club this term, scoring four goals and bagging four assists to help the side remain in contention for a spot in next season's Champions League.
His performances also saw Sane earn his first call-up to the Germany national squad in November where he would earn his first cap during the friendly with France.
Despite the youngster's progress, there will inevitably be an element of risk for any side willing to part with the kind of fee required to sign him from Schalke, even if the price is much lower than initially thought.
While City's acquisitions of Kevin De Bruyne for £55m (via BBC Sport) and Raheem Sterling for £49m (via BBC Sport) perhaps mean there will be less pressure on Sane should he move to the Etihad - as he would be some way off their most expensive acquisitions - a switch to Anfield would arguably see the youngster under immense strain to perform, especially given how the likes of Christian Benteke (via BBC Sport) and Roberto Firmino (via BBC Sport) have fared since their big-money moves.