The sought-after striker is thought to be attracting interest from Manchester City as the Blues may lose Carlos Tevez, possibly as part of the El Shaarawy deal if reports are to be believed.
And although Galliani is adamant he wants to keep one of his most prized assets, he knows that should a tempting offer come in then he would have to consider it.
"El Shaarawy is the most sought-after player on the market but I have not yet received any proposal," he told Gazzetta dello Sport.
"But I cannot rule out he could be sold, because in this market everything can happen."
However, El Shaarawy's agent Roberto La Florio insisted that there is nothing in the rumours, and that his client is happy at Milan.
"The player is fine and he hopes to stay at Milan," he told Sportitalia.
"Offers from City? Nobody called me."