Local news agency Ansa claim that police were called to a pub in Rome ahead of Tuesday night’s Champions League tie at Stadio Olimpico.
The Chelsea fans are not believed to have suffered any injuries, with the aggressors having dispersed once security forces arrived on the scene.
Police are yet to release a statement on the matter and neither club have commented.
While hoping to avoid further disturbances off the field, Chelsea are readying themselves for another tough test on it.
A thrilling reverse fixture at Stamford Bridge saw the two sides share six goals in a 3-3 draw, with Eden Hazard rescuing a point for the Blues.
Antonio Conte faces some tough selection decisions heading into the return date, with a number of players nursing knocks, while the Italian also has a home date with Manchester United on Sunday in the back of his mind.
"It's important for us to overcome this difficult period," the Blues boss told reporters ahead of a trip to Rome.
"We are recovering important players, and you know very well how important it is for me to have all the players available.
"Whenever you are playing seven games in 21 days, you don't sort problems out overnight. You just have to try and do your best in every game to face this emergency. We've faced this situation since the beginning of the season. I hope it ends soon.
"There are two big games before the international break, against Roma and then United on Sunday.
“For us, for sure, two big games. But I like to repeat that the most important thing is to go game by game. The most important game is against Roma.
"Which will be the final result? I don't know. But we have to put all [out of] ourselves to try and get a good result. That will be really important, a good result. And then we must try and prepare for another tough game against United in the league."
Chelsea have collected seven points from their three Champions League fixtures so far to sit top of Group C.