The Italian side, keen to sign the Spain frontman, are seeing if the Blues would take Mattia Destro as part of any deal.
Torres has struggled for form since moving to Stamford Bridge from Liverpool in a £50million deal back in January 2011.
Manager Jose Mourinho has bolstered Chelsea's attacking options this summer with the signing of Atletico Madrid striker Diego Costa for £32million while Blues legend Didier Drogba also returned to the club.
Roma already have one former Chelsea star amongst their ranks having signed left back Ashley Cole on a free transfer.
