The 23-year-old was strongly linked with a move away from Stamford Bridge over the summer, but the window closed with the defender remaining in London.
Chalobah has another four years left to run on his contract with the Blues, having signed a contract extension last November, but there is currently uncertainty surrounding his future at the club.
The former England Under-21s international has only featured once this season, playing the full 90 minutes against Leicester City in the Premier League on August 27.
Chalobah was also an unused substitute against Red Bull Salzburg in the Champions League last week, which proved to be Graham Potter's first game in charge of the club.
According to Football Transfers, the defender is likely to leave the Blues on loan during the January window, and Roma are currently at the head of the queue for his services, with the club's head coach Jose Mourinho keen on a deal.
The report claims that Aston Villa had been interested in his signature over the summer, but Steven Gerrard's side are no longer in the running, with Roma the front runners at this stage.
Inter Milan and AC Milan are also said to have looked at signing Chalobah during the recent transfer market before moving on to other targets.
A permanent exit is allegedly not being considered by Chelsea at this stage, but the club are willing to let him leave on a short-term basis when the winter window opens for business.
"I feel that when the chance comes, it comes," Chalobah told talkSPORT last week. "I will always be patient because playing for a club like this is not easy, there is always going to be competition.
"That is the best thing for all the players and for me, training with the best players day in, day out. I try not to focus on the outside noise and focus what I'm doing and what I want to do this season. That is to get myself into the team and play a lot of games this season."
Chalobah had loan spells at Ipswich Town, Huddersfield Town and Lorient before becoming a first-team regular for Chelsea during the 2021-22 campaign, making 30 appearances in all competitions.
The Blues had a defensive turnaround over the summer, with Malang Sarr, Antonio Rudiger, Andreas Christensen and Marcos Alonso among those to leave, while Wesley Fofana, Marc Cucurella and Kalidou Koulibaly arrived at the club.