Serbia centre-back Nastasic has fallen out of favour at the Etihad Stadium this season, with his only appearance coming in the 3-0 Community Shield loss to Arsenal back in August despite the defending Premier League champions suffering a number of injuries at the heart of their defence.
Schalke now appear ready to offer the 21-year-old an escape route, with general manager Horst Heldt revealing that discussions with Nastasic's advisors have already taken place.
Heldt told Bild: "We are very interested and his advisers, who are in England, are in initial talks with Manchester City."
Bild report that the proposed deal for Nastasic would be a loan with an option to buy.
Nastasic has made 34 Premier League appearances for City since joining from Fiorentina in August 2012, helping Manuel Pellegrini's side to the their second English top-flight crown in three seasons last term.
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