The 21-year-old has been plagued by injury problems this season - having made only one start in Serie A - as the Rossoneri have endured a disappointing campaign so far.
The Italy international revealed he rejected the chance to leave San Siro last month, claiming he wants to win silverware with Clarence Seedorf's side.
"There has been an offer from a Russian team, but I decided to stay at Milan because that’s what I want," El Shaarawy told Corriere dello Sport. "It’s my intention to become a champion here."
Massimiliano Allegri was replaced by Seedorf as coach in January amidst their turbulent 2013-14 campaign and El Shaarawy is determined to be a part of a new era at San Siro.
"I’ve been dogged by bad luck," he added. "In September I had a muscular problem and since then I have had a succession of niggles.
"And it culminated in December with the operation on my foot. It’s important for me to get back to Milanello as soon as possible and try to heal.
"It’s been a difficult few months, what with the injury and the coaching change. I owe Allegri a lot - he immediately gave me confidence when I came into the team.
"But I’ve had Seedorf as a team-mate and he helped me in the locker room in the past. I know he can do a great job.
"I’ve never felt excluded from this team, even when I was at my lowest with injury."
Milan sit 11th in Serie A, seven points behind fifth-placed Inter.