Former Bayern Munich boss Pep Guardiola has earmarked Sane for his debut campaign at the Etihad Stadium, though Schalke had been keen to keep hold of the Germany international.
Having broken into the Schalke side in 2014-2015, Sane cemented his place last term, scoring eight times in 33 Bundesliga appearances.
City has already added Ilkay Gundogan, Nolito and Oleksandr Zinchenko to its squad, with Sane now likely to become its fourth new recruit.
"Leroy has clearly stated that he wants to leave this summer," general manager Christian Heidel said.
"We have to accept this.
"We will only discuss a transfer if the conditions are best for Schalke."