The Spaniard's team were crowned champions on the final day thanks to a 4-1 victory at Brighton & Hove Albion which took them to 98 points, the second-most ever reached in a PL season behind only the 100 they themselves managed last term.
Liverpool fans were understandably not happy with the song.
The club have firmly denied that the "battered in the streets" lyric refers to Cox, a Meathman and Liverpool supporter who was left with brain injuries after being assaulted outside Anfield by Roma ultras in April past year.
However, City have long claimed "the attempt to damage the club's reputation is organised and clear" and said they "will not be providing any comment on out-of-context materials purportedly hacked or stolen from City Football Group and Man City personnel and associated people".
Cox sustained brain injuries following an attack in the build-up to Liverpool's Champions League semi-final with Roma previous year, with three Italians sent to prison for their offences.
And his brother, Martin, has said that he was "disgusted" by the chant.
When asked if it annoys him that he is now behind the City boss, Mourinho told L'Equipe: "No, no, this reminds me that I'm there with 25 titles".
Sean Cox is now receiving treatment at the National Rehabilitation Hospital in Dún Laoghaire.
According to the report, a UEFA decision could be delivered this week but added that it's still not clear if the exclusion would impact on next seasons competition or would see the Citizens omitted from the 2020-2021 Champions League.
The song cites fans being "battered in the streets" and "crying in the stands" and includes a line on Liverpool forward Mo Salah being injured - but with the original culprit, Real Madrid's Sergio Ramos, changed to City defender Vincent Kompany.
City, however, have since issued a statement clarifying: "Any suggestion that the lyrics relate to Sean Cox or the Hillsborough tragedy is entirely without foundation".