The Spaniard has failed to live up to expectations following his £50m arrival from Liverpool in 2011, leading to speculation that he may be allowed to move on.
These rumours have increased in intensity in recent times, with the Blues being strongly linked with a move for Atletico Madrid’s Radamel Falcao as well as signing Demba Ba.
This has alerted the Florence-based side, who are keen to draft in a big name centre-forward to kick-start a new era of success at the club.
Fiorentina director Eduardo Macia, who was instrumental in taking Torres to Anfield from Atletico, has highlighted the 28-year-old as their top target.
There are concerns surrounding wage demands, but the club are exploring avenues to accommodate the striker.
One option they attempt to utilise would be a deal for Chelsea to contribute to his pay packet for the remainder of his contract at Stamford Bridge.
They struck a similar deal with Liverpool to take Alberto Aquilani to the club, with the Reds keen to move the Italian flop on and free up space in their squad.
Chelsea may be willing to accept such demands, with owner Roman Abramovich keen to slash the Londoners’ wage bill.