The Turkish newspaper AMK state that the Istanbul giants want to loan the former Germany international on a season-long loan which will include an option to buy.
Schweinsteiger has been omitted from United’s squad by manager Jose Mourinho however, Galatasaray will struggle to match his £275,000-a-week wages.
The Istanbul giants do however, face competition from Istanbul rivals Besiktas according to the Express. A source close to Besiktas did however, tell Turkish-football.com that the club a move looks unlikely considering his current wages.
Schweinsteiger managed just 13 Premier League starts for Man Utd last season and was plagued with knee injuries.
Galatasaray have also been closely linked with Liverpool midfielder Lucas Leiva, Arsenal full-back Mathieu Debuchy and Newcastle defender Daryl Janmaat.