Neither player has been in Mauricio Pochettino's plans this season, as both are yet to make an appearance for the club under the new manager.
A thigh injury has kept Chalobah out for the past few months, but after transfer speculation over the summer, he is likely to leave the club in the near future.
Sarr has not been diagnosed with any injury of his own, but he has not featured in a single matchday squad in any competition for Chelsea this season.
The return of Levi Colwill from his loan spell at Brighton & Hove Albion and arrival of Axel Disasi from Monaco has seen the pair slip down the pecking order, and Mourinho and Roma are reportedly taking notice.
Calciomercato claim that Mourinho is targeting the defenders, both of who are experienced at playing in a back three, which the manager has implemented at Roma.
Chalobah would join former Chelsea teammate Tammy Abraham in the Italian capital, as well as fellow English defender Chris Smalling.
Sarr is no stranger to changing scenery either, as he has had spells at Porto and Monaco on loan since joining Chelsea from Nice in 2020.
Having only kept four clean sheets in their opening 12 Serie A matches this season, Mourinho is evidently prioritising defensive reinforcements to bring more balance to a side that has strength in attack in the form of Romelu Lukaku and Paulo Dybala.
Smalling's injury woes have meant that Gianluca Mancini, Evan Ndicka and Leeds United-loanee Diego Llorente are the only senior centre-backs in the squad.
Roma have struggled slightly this season in general too, as a draw in the Derby della Capitale against Lazio before the international break kept them outside the European places.
Another European run could be on the cards though, as they are favourites to progress from their Europa League group after winning their opening three games.