The 20-year-old, who has a contract with the Rossoneri until June 2018, has been linked with clubs such as Borussia Dortmund and Manchester City over this season.
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"I am feeling very good at Milan and I hope to stay here for the rest of my life," the Italy international told La Gazzetta dello Sport.
"I heard what Galliani said about me and it pleases me that the club do not want to sell me."
El Shaarawy then went on to discuss his poor form in recent months after a superb start to the 2012-13 campaign - though he has netted 16 goals in 33 Serie A appearances so far this term, the forward has not scored since the derby against Inter on February 24, a source of frustration.
"I was disappointed on Sunday after the match against Catania as I had some good chances but didn't score," he added.
"Obviously I miss the feeling of finding the net. I'm an attacker and forwards always want to score."