Manchester City and Manchester United have both been linked with a swoop for young striker El Shaarawy, who has started the new Serie A season in superb form.
Galliani insists there is no chance of Milan letting El Shaarawy leave, while he is keen to sort out a new deal to keep him at the San Siro for another six years.
"Manchester City and United interested in El Shaarawy? It's no joking matter! Stephan has a contract with us for other five years and soon he will extend until 2018," said Galliani.
While El Shaarawy has been linked with a move from Milan to Manchester City, there has again been speculation about Mario Balotelli heading in the opposite direction.
Galliani admits he is an admirer of the former Inter Milan player, but is staying realistic about the chances of agreeing a deal.
He said: "I have a profound love for Balotelli, but love doesn't always end well."