Sane is highly rated in Germany and has been linked with a big money move away from Schalke.
The Bundesliga side are said to €40 million for the teenager (in the region of £32 million), but City have reportedly stepped up their interest and hope to deal this January, but the report suggests that a summer move is the more likely prospect.
He has been on the club's radar since December 2013 and the asking price would not be beyond Manchester City's spending power as has been seen in recent transfer windows with big fees for Kevin De Bruyne and Raheem Sterling during the last window.
City are not the only Premier League side reportedly interested in landing the youngster, with the Liverpool Echo reporting that Jurgen Klopp was monitoring the player last month, as they reported Klopp was 'considering his options' ahead of the January window. Nothing much more seems to have happened on that front.
But given the asking price that appears to be mooted by The Guardian's report linking Sane with City, it would seem a little steep and may price Liverpool out of the game. If the Reds were to do a deal themselves, it may take a lot of persuading on the part of the manager.
The other figure mentioned is £25 million which would be more in Liverpool's price range but given the superior spending power of Manchester City, and the club's current stature in that they can offer Champions League football, one would imagine they would be the favourites out of the two Premier League clubs to land his signature.