Torres, who cost Chelsea an eye-watering £50million in 2011, failed to recapture his Anfield form which made him one of world football's deadliest hitnmen, and the summer arrivals of Diego Costa and Didier Drogba made his status at Stamford Bridge redundant.
Mourinho has already allowed three strikers to leave since the end of last season, with both Samuel Eto'o and Romelu Lukaku joining Everton whilst Demba Ba linked up with Turkish side Besiktas.
However, the Special One has made it clear that he intends to go through the upcoming Premier League campaign with three strikers in his squad, and will now make a move for one of Falcao, Remy or Bony before the transfer window shuts on Monday evening.
Top of Mourinho's list is France international Loic Remy, who has a bargain buyout clause of £8.5million.
Fernando Torres Player Profile
Despite the fee, there are doubts over the Frenchman's long-term fitness, as highlighted by a collapsed move to Brendan Rodgers' Liverpool.
Also attracting Chelsea's interest is Colombia international Radamel Falcao, who is available from Monaco on a season-long loan.
However, the former Atletico Madrid star is being chased by Arsenal and Real Madrid, and may not fancy competing with Costa for a place in the starting XI.
Chelsea's final target is Ivory Coast international Bony, who is highly valued at Swansea.
The Welsh club have reportedly slapped a £24million price-tag on the powerful forward, which could dissuade Mourinho from making an enquiry.