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Violence erupted between a group of 50 rival fans on a bridge near the Stadio Olimpico in Rome.
Police used two baton charges to disperse the fans. It is not known if any British nationals were arrested.
The last time the two teams met in April, 11 fans were taken to hospital after violence in the stadium. The stab injuries are not said to be serious.
Consular officials are at the hospital where the fans have been taken. It is reported that two others, one of them a 16-year-old boy, needed treatment for the effects of drink.
A Foreign Office spokesman said the situation outside and inside the stadium was "calm."
He said: "It appears there was trouble outside the stadium.
"A number of British fans were injured and two British nationals have been arrested.
"Our consular officials are on the way to the hospital to check on conditions, the numbers involved and whether anyone needs assistance.
"The situation is now said to be calm both outside and inside the stadium."
The violence flared at the Pont Duca d'Aosta bridge, the scene of many clashes between visiting fans and Roma's Ultras contingent.
Last season there was trouble during the two clubs' Champions League game in Rome when fans were charged and beaten by riot police trying to regain control in the stadium.
Scuffles also broke out outside Old Trafford during the second leg of the tie, with 21 people arrested.
Greater Manchester Police officers travelled to Rome before Tuesday's game and issued a warning to hooligans not to attend.