Footage has surfaced online of members of the playing squad and backroom team chanting a parody version of 'Allez Allez Allez', a song adopted by Liverpool supporters that was frequently heard at Anfield during the 2018-19 campaign.
The altered version of the song, that is filmed on board a plane, presumably transporting City players and staff from Brighton after their Premier League title triumph on Sunday, mocks Liverpool as "victims of it all" and that they're "battered on the streets".
City have, however, denied that the lyrics relate to Reds fan Cox, who was violently attacked outside Anfield prior to last season's Champions League win over Roma, or the Hillsborough disaster.
"The song in question, which has been a regular chant during the 2018-19 season, refers to the 2018 UEFA Champions League final in Kiev," a City spokesperson said.
"Any suggestion that the lyrics relate to Sean Cox or the Hillsborough tragedy is entirely without foundation."
The chant also mentions the injury suffered by Mohamed Salah in the 3-1 defeat to Madrid, with Sergio Ramos's strong challenge ending the Egyptian's participation in that game midway through the first half.
The words in the version recorded featuring City staff and players are changed from Ramos to Vincent Kompany, seemingly relating to the City captain's tackle on the 26-year-old in his side's 2-1 win over Liverpool back in January.
Pep Guardiola's side edged out the Reds in the race for the Premier League title in 2018-19, winning their second consecutive league crown after finishing a point above Jurgen Klopp's men.
City had trailed against Brighton in Sunday's finale, only for goals from Sergio Aguero, Aymeric Laporte, Riyad Mahrez and Ilkay Gundogan sealing a 4-1 win at the Amex Stadium.
That meant that Liverpool, who beat Wolves 2-0 in their last match of the league campaign, would finish on 97 points, one behind their rivals for the title.
Despite coming up short in the title race, Liverpool can still win a trophy in 2018-19, with Klopp's side facing Tottenham in the Champions League final on June 1.