Pep Guardiola's men put one hand on the Premier League title after their 2-1 win at Old Trafford on Sunday (10 December) saw them steer 11 points clear of the home side.
The celebrations soon began for the visitors with Leroy Sane tweeting a post-match picture of the City players with confetti in the dressing room.
According to Manchester Evening News, Mourinho visited the City dressing room and told the players to tone down their celebrations and to celebrate in a more dignified manner.
This resulted in an altercation with City goalkeeper Ederson, whose double-save during the second-half proved pivotal, as the two got into a shouting contest in Portuguese.
The same report claims Mourinho had water thrown at him while City captain Vincent Kompany attempted to defuse the situation.
A Mirror report states that as a result of the altercation, members from both teams approached the dressing room. United striker Romelu Lukaku and goalkeeping coach Silvino Louro were also said to be involved in the incident.
Former Arsenal midfielder Mikel Arteta, now part of Guardiola's coaching staff at City, was also said to have suffered a cut above his eye that left his face bloodied, most likely from a bottle.
The incident had shades of the infamous Battle of the Buffet back in 2004 when United manager Sir Alex Ferguson had a pizza slice thrown at him by Arsenal's Cesc Fabregas when the Gunners' 49-match unbeaten run came to an end at Old Trafford.
City's win saw them equal the English top-flight record of 14 consecutive wins set by Arsenal in 2002 while the Citizens also set a new benchmark for most consecutive victories in the same season.