The AC Milan CEO says the young forward is the subject of plenty of interest but denies the club are in negotiations to sign Carlos Tevez
The young striker helped the club to a top-three finish with some fine early-season performances but faded badly in the second half of the campaign.
The likes of Manchester City have been credited with an interest in the player and the 68-year-old hinted that he could be sold.
"El Shaarawy is the Milan player with the most requests," he told Sky Italia.
"He's not unsellable because everything can happen in the transfer market."
Meanwhile, Galliani has denied recent reports that the club are in talks with City star Carlos Tevez.
"There are no negotiations with Tevez," he added.
Finally, Galliani claimed that Kevin-Prince Boateng has not requested a move away from San Siro, adding: "Boateng did not ask to be sold."