Despite the lucrative offer, Galliani insists that El Shaarawy has no interest in leaving Milan.
"What we hadn't told anyone was that we received a very big offer for El Shaarawy, but I will never name the club involved," Galliani told Italy's 7 Gold Television. "It is a very important club, though.
"I informed the player's agent and as soon as he returned from the Confederations Cup, I spoke to Stephan. We did not want to sell him, so we simply informed the lad and his family that this proposal had arrived for him.
"I asked him what he wanted to do. He said the money he had was more than sufficient, that he is a Milan fan and did not want to leave. I kissed him on the cheek and that was that."
El Shaarawy scored 18 goals for Milan last season.