That is according to The Times, who claim Blues boss Antonio Conte has not given up hope of signing the 31-year-old.
Chelsea were heavily linked with Bonucci over the summer as Conte sought new defenders in his first transfer window at the club.
But Juventus slapped a huge £50million price tag on the centre-back's head to deter suitors.
Chelsea instead re-signed David Luiz for £32m on deadline day but the Brazilian's return has not sured up Conte's defence.
The club have conceded nine goals in their last four games and have not won a match since the window closed at the end of August.
It was claimed yesterday that Conte plans to overhaul the Chelsea squad in January and that centre-back Gary Cahill could be axed.
Cahill considered leaving Chelsea midway through last season when his place in the England team was under threat by his lack of first-team __football at Stamford Bridge - but he eventually stayed on at the club.
Replacing Cahill with Bonucci could prove expensive for the Blues.
Cahill still has three years left of his £85,000-a-week deal in west London, while Juventus have offered Bonucci a new contract.
Juve manager Massimiliano Allegri is keen to retain the defender, who has been pivotal in Juve's recent dominance of Italian football, and negotiations over a contract running until 2021 are supposedly ongoing.
However, the Daily Mail claimed earlier this week that Chelsea owner Roman Abramovich is willing to finance big-money moves in the New Year.