The Blues were linked with the experienced Italian over the summer, amid rumours that he had grown unsettled at the Stadio Olimpico.
A deal failed to come to fruition, however Jose Mourinho is thought to have remained keen on the midfielder.
‘The Special One’ is believed to have made a striker his main target for the transfer window, but he is also keen to land a central player to boost his side’s tilt at the Premier League title.
De Rossi – Roma’s vice captain – is seen as the ideal candidate to add some authority to the Blues’ engine room due to his commanding presence.
Mourinho is also attracted to the 30-year-old’s experience, with the player holding over 90 international caps.
A potential stumbling block could be Roma’s eagerness to keep their talismanic midfielder, with the capital-based side firmly in the hunt for the Serie A title after an impressive start to the campaign.
De Rossi is a product of the Rome club’s academy set-up, and has made in excess of 300 outings in the red shirt.