The AC Milan striker has been recuperating from a fractured metatarsal and hasn't featured for the Serie A giants since January.
Reports abounded at the back end of last year that the Gunners could sign the 22-year-old for as little as £11.5m.
But El Shaarawy has shut the door on a summer move to the Emirates.
Arsenal - Most Expensive Transfers
I am gratified by Arsenal interest, certainly, but my objective is to come back for Milan
Stephan El Shaarawy
"I am gratified by Arsenal interest, certainly, but my objective is to come back for Milan and do well at Milan," he told Tuttomercatoweb.
El Shaarawy also provided a positive update on his rehabilitation when he said: "I am recovering well, later this week I should be removing the cast and then the rehabilitation process can begin."
The Italian has scored just once in 17 appearances for Milan this term.
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