If the transfer goes through, and hits the 50 million mark, it would make Sane the most expensive German signing of all time.
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"We have now cleared things up with Manchester. Now Manchester must clear things up with the player," Schalke's director of sport Christian Heidel told local newspaper WAZ.
The 20-year-old is a rising star in the Germany squad and has already posed for pictures with City fans in Manchester.
The reported transfer figure seems astronomical given that Sane has made just 47 Bundesliga appearances, scoring 11 goals and creating seven more, since his debut in April 2014.
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The fleet-footed forward made the last of his four international appearances for the world champions as a late replacement in last month's 2-0 defeat to hosts France in the Euro 2016 semi-finals.
Sane, who scored eight goals in 33 Bundesliga games last season, was missing when Schalke flew to their pre-season training camp in Austria on Monday.
The Royal Blues had confirmed his trip to Manchester where he is expected to sign a five-year deal to work under City's new coach Pep Guardiola.
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