City, Swansea and Watford are all looking at the 22-year-old who is in the final year of his contract at Stamford Bridge, according to ESPN reporting "sources close to the player".
Chalobah has spent time on loan at Watford, Nottingham Forest, Middlesbrough, Burnley, Reading and Napoli during his time at Chelsea, but if he is not guaranteed regular action he could decide to move on.
As noted in the report, the Premier League champions are being heavily linked with completing a swoop for Monaco midfielder Tiemoue Bakayoko next week, and that will only push Chalobah further down the pecking order.
Chalobah is one of a number of promising Chelsea players finding it impossible to break into the first-team and being sent out on loan to clubs across Europe. The Sun claim that he is seeking assurances from Antonio Conte, with regards to his chances of regular first-team football, before signing a new deal with Chelsea.
Leicester are also keeping tabs on Chalobah as they look to freshen up their squad after a disappointing campaign last term and Chalobah is sure to have no shortage of offers if he does decide to leave Chelsea.