Returning Blues boss Jose Mourinho is anxious to land a world class centre-forward despite Torres' recent revival - the club's record signing netted 22 times last term and recently finished top scorer at the Confederations Cup in Brazil.
The Portuguese's main target is Napoli hitman Edinson Cavani, but Chelsea are yet to meet the Italian club's asking price.
And should the Special One fail to sign the Uruguayan he will instead raid Serie A for El Shaarawy, who scored 19 goals in all competitions last season.
The 20-year-old, who is of Egyptian descent, is already a regular for Italy at senior level and has been tipped for big things.
Milan are understandably reluctant to let him leave, though, and will demand Torres switches to the San Siro if Chelsea firm up their interest this summer.