The Foreign Office confirmed it was in contact with the French authorities over the incident.
The English giants on Wednesday made history as the first ever club to overturn a 2-0 home defeat against PSG by winning the return leg 3-1 to book a place in the quarter finals, courtesy of the away goal rule.
A Manchester United fan was reportedly celebrating the victory in a taxi was stabbed.
He is being treated at the Georges Pompidou European Hospital in Paris but is expected to be released on Sunday or Monday.
"We are in touch with the French authorities following an incident involving a British man in Paris on 6 March and stand ready to offer assistance if required," the Foreign Office said in a statement.
The fan was reportedly in a taxi celebrating the victory when the incident happened.
"We were shocked to hear about the incident with one of our fans who was stabbed while in Paris for the Champions League game," a Manchester United spokesperson said.
"Everyone at the club wishes him well during his recovery."