Chelsea owner Roman Abramovich wants their new manager settled within a month.
Il Giornale says Chelsea are focusing on Italian pair Antonio Conte and Massimiliano Allegri.
Chelsea officials have twice met with Conte since Christmas, while Juventus boss Allegri has impressed the Blues hierarchy for his work in Turin.
Conte is now regarded ahead of Allegri in the running, though he also counts on interest from AC Milan, PSG and Juventus.
It's suggested Abramovich wants their permanent manager identified by mid-March.