Silva, 31, will leave the Etihad Stadium as a free agent this summer after nine seasons that brought him 19 major trophies, including six Premier League titles and a Champions League.
His priority has consistently been a move to Barcelona, where he has been identified as a key target by sporting director Deco. But those talks have stalled, with Barcelona asking for more time to structure their transfer budget before committing, and Galatasaray have moved into that space.
According to Turkish reports, the Istanbul club approached Silva's agent Jorge Mendes with a package worth €15 million per year — a figure no European club is currently prepared to match. The offer is designed to place him alongside Victor Osimhen, Leroy Sané and İlkay Gündoğan, the latter two being former Manchester City teammates who made the same move to Istanbul last summer.
Silva's preference remains Barcelona. He is understood to be waiting for clarity from Deco's office before committing elsewhere, but the longer that clarity takes to arrive, the more credible the Galatasaray alternative becomes.
Juventus have also made contact with Mendes, offering a three-year deal worth around €7 million per year — a figure contingent on them securing Champions League qualification. AC Milan are monitoring the situation too.
Silva contributed three goals and five assists across 44 appearances for Manchester City this season. His departure will prompt one of the most competitive free-agent pursuits of the summer window.