The 19-year-old winger, who joined the San Siro outfit from Genoa in 2011, has already scored four Serie A goals in six appearances this term.
But Galliani says that, whilst it is encouraging that El Shaarawy is being admired by such a big club, Milan are not contemplating selling him at any point in the near future.
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"I'd like to give peace of mind to supporters, considering we have recently renewed his deal until 2017."
The player's agent, Roberto La Florio, also recently deniedthat he had been in contact with the Red Devils and is adamant that his client is happy in Italy.
"I have had no contact with the United. The player has been secured by AC Milan and he is happy to play for them. He has always dreamed it," La Florio told tuttomercatoweb.com.
"He has to keep both feet on the ground, thinking about this club which trusted in him, and that he is paying off with these performances."