The 21-year-old’s agent Roberto La Florio has suggested that the Little Pharaoh could join the current Turkish Super League champions after falling down the pecking order at the San Siro this season.
“Galatasaray are a big club, they play in the Champions League and are very ambitious,” La Florio told Turkish radio station Radyospor.
“If Galatasaray are interested then obviously we would consider any offers made.
“It’s an honour for a manager like [Roberto] Mancini to be interested in El Shaarawy and if our terms were to meet we would be open to talks.
“However, for the time being Stephan is keen to continue at Milan.”
El Shaarawy has also been closely linked with several English Premier League clubs including Arsenal, Chelsea, Liverpool and Manchester City.