The 19 year old has scored four times as his side have taken seven points from their opening six matches.
"Let's hope Ferguson will stay in love with him, but it's not in our thoughts to sell him," said Galliani.
"I'd like to give peace of mind to supporters, considering we have recently renewed his deal until 2017."
El Shaarawy has emerged as one of Milan's brightest prospects after being snapped up from Genoa in June 2011.
His agent Roberto La Florio has also quashed rumours of a potential Old Trafford switch.
"I have had no contact with the United," he told tuttomercatoweb.com. "The player has been secured by AC Milan and he is happy to play for them. He has always dreamed it.
"He has to keep both feet on the ground, thinking about this club which trusted in him, and that he's paying off with these performances."