The Blues appear keen on landing a new forward, but their inability to have an offer for Napoli's Edinson Cavani accepted has forced them to look elsewhere.
Recent reports have suggested that Fiorentina's Stevan Jovetic and Borussia Dortmund's Robert Lewadowski are on the west London club's radar.
However according to TalkSPORT it is the Italian international who is in their sights.
According to the radio station, Jose Mourinho is grown anxious over Chelsea's inability to land a world-class forward and will push for a move to land El Shaarawy.
However Milan are unlikely to let the 20-year-old leave and will reportedly demand Torres in return for doing just that.
Torres has never fully hit his best form with Chelsea since joining the club in 2011, but showed glimpses of his best in the Europa League in particular, helping his club lift the trophy with victory over Benfica in the final.
Manchester City have previously been linked with a move for El Shaarawy.
Despite the fanciful nature of TalkSport's claims, El Shaarawy, who only extended his contract until 2018 in February, could well be on the move this summer.
AC Milan's vice-president Adriano Galliani has revealed he will hold talks with the talented youngster over his future upon his return from Brazil.
I'm going to talk to him on Tuesday," he told Sky Sports Italia. "We've got lots of players and before we can buy anybody, we've got to sell."
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