Gala's Italian manager Roberto Mancini is chasing the young forward for the winter market.
Speaking to Radyospor, Roberto La Florio said: "Galatasaray are a big club, they play in the Champions League and are very ambitious.
"If Galatasaray are interested then obviously we would consider any offers made.
"It's an honour for a manager like Mancini to be interested in El Shaarawy.
"If our terms are met we would be open to talks.
"However, for the time being El Shaarway is keen to continue at AC Milan."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball