The 20-year-old has been one of the revelations of the 2012-13 campaign, netting 16 goals in 37 Serie A appearances, and has recently been linked with a move to the Premier League runner up.
El Shaarawy is keen to stay at Milan, though, and is not interested in a move to City for now.
"It is flattering if Manchester City really want me, but I want to stay here. I don't think that I will leave Milan," the Italy international told La Repubblica.
"I have always felt that everybody at the club believes in me, the coach, the direction and my teammates. I also have them to thank for breaking into the national team."
Milan CEO Adriano Galliani, meanwhile, has insisted the young forward is going nowhere, while former Rossoneri striker Filippo Inzaghi has advised him to stay put.
"El Shaarawy is untouchable, he's not leaving Milan," said Galliani.
"He should stay at Milan. He can still grow as a player here," added Inzaghi.
El Shaarawy signed a new contract with Milan until 2018 earlier this year.