Galliani told 7 Gold television of the offer.
"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. It is a very important club, though," said Galliani.
"I informed the players' 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.
"We were not tempted by the offer, but we couldn't exactly hide it from him. He saw the figures, but did not want to budge. How big was the offer? More than 30m."