The 30-year-old has endured a miserable spell at the west London club, scoring just 20 goals in 110 league appearances, and has been targeted by Roma in a deal that would see highly-rated striker Mattia Destro move in the opposite direction, The Times reports.
Torres was forced to watch from the sidelines as compatriots Costa and Cesc Fabregas earned plaudits for their stand-out performances in the 3-1 defeat of Burnley at Turf Moor on Monday.
The Spaniard signed for Chelsea for £50m during the January transfer window of 2011 after handing in a transfer request at Anfield.
But he has failed to recapture the electrifying form he showed on Merseyside and has been pushed towards the exit door with the arrival of Costa and Drogba.
The Blues were reportedly looking for suitors for Torres in the summer but have so far failed to find a club willing to pay a transfer fee and match his £180,000-a-week wages.
Destro has been touted as a future leader of the Italian national front line after he was axed from Cesare Prandelli's World Cup squad despite making the provisional 30-man list.
He has so far scored 19 goals in 41 appearances for the Rome club after moving to the Italian capital from Siena in 2012.
Rome have already taken Ashley Cole, another Chelsea cast-off who joined the Giallorossi with Mourinho's blessing.
- Sports & Recreation
- Fernando Torres
- Diego Costa
- Didier Drogba
- Jose Mourinho
- Mattia Destro