The Rossoneri vice-president refused to name the club that attempted to lure the 20-year-old forward from San Siro but says that he ran the offer by the Italy international, who did not want to leave the Serie A side.
"What we haven't told anyone is that we received a very big offer for El Shaarawy, but I will never name the club involved," the 68-year-old told the 7 Gold television network.
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"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 [that he] 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.
"We discussed tactics for next season, as we are returning to a 4-3-2-1 system and he is happy to play as a support striker.
"He had a goal-scoring crisis in recent months, not a physical one, but he always worked hard for the team.
"He is only 20, so some ups and downs are natural. It even happened to Edinson Cavani, who didn't score for two months."
El Shaarawy, who was crucial in the first half of last season for Massimiliano Allegri's side before suffering a dip in form in 2013, has a contract at the club until 2018.