The 20-year-old's future was put into question as manager Massimiliano Allegri has signed forwards Alessandro Matri from Juventus and Kaka from Real Madrid over the last four days.
Following the departure of Zalatan Ibrahimovic to Paris Saint-Germain in 2012, El Shaarawy took centre stage in the Milan attack, scoring 16 league goals as the Rossoneri finished third in Serie A.
Despite the introduction of Matri and the return of Kaka, El Shaarawy believes he can still contest for a place in the starting XI.
"I've decided to stay at Milan," he told Sport Mediaset as he arrived in Florence to join the Italian national squad.
"I have made a precise decision and, no matter what offer arrives, I want to stay at Milan.
"There's more competition in the squad now, but there will be playing time for everybody. I'll fight for my place in the team."
El Shaarawy was dropped from the Milan side which beat Cagliari 3-1 at the San Siro on Sunday, but the forward understands the competition in the squad, saying; "I don't question the decisions of the coach."