The 24-year-old is facing an uncertain future in West London as he has allegedly been told by the Blues that he is free to leave in January.
Chalobah is yet to feature under Mauricio Pochettino this season due to a thigh injury and is continuing to undergo his rehabilitation programme following a setback in training last month.
The versatile defender has made a total of 63 appearances for Chelsea across all competitions since and including his debut in 2021, including 34 outings last season.
However, it is thought that Chalobah could struggle to earn regular game time in the Chelsea first team when he returns to full fitness.
Pochettino has regularly selected summer signing Axel Disasi, Thiago Silva and Levi Colwill in his defence, while injured duo Wesley Fofana and Benoit Badiashile are both believed to be in the long-term plans of the Argentine boss.
Borussia Dortmund have allegedly been offered the chance to sign Chalobah in January, while Thomas Tuchel's Bayern Munich have also been credited with an interest.
However, according to Sky Deutschland reporter Florian Plettenberg, both German clubs have decided to pull out of the race for Chalobah's signature.
Plettenberg has suggested that Chalobah's injury concerns are one of the factors behind the decision of the Bundesliga pair to end their pursuit of the defender.
The decision of Bayern and Dortmund to walk away from a proposed deal for Chalobah has seemingly opened the door for a number of other clubs to step up their interest including Jose Mourinho's Roma, who are believed to be eyeing up a winter-window swoop for the Englishman.
Roma's interest in Chalobah, as well as Malang Sarr, comes at a time when centre-back Chris Smalling has been linked with a potential exit amid interest for Saudi Arabia.
The Serie A side could face stern competition from Premier League clubs in the race for Chalobah, though, as Manchester United, Tottenham Hotspur and West Ham United are all understood to be considering a move for the defender.
Chalobah, who is believed to be valued by Chelsea in the region of £45m, is under contract at Stamford Bridge until summer of 2028.