The Premier League champions say there is no truth to the suggestion, which surfaced in Spanish newspaper Mundo Deportivo, that Pep Guardiola tried to persuade Messi to move to the Etihad Stadium on a deal that would have been worth more than £1 million per week.
City chairman Khaldoon Al Mubarak was asked at a recent Q&A event which transfer near-miss he most regrets from his 10 years with the club.
A video posted to Twitter shows he replied, while laughing, "Messi".
On Saturday, however, Mundo Deportivo ran an updated story, including quotes supposedly made by Al Mubarak, that revealed further details of City's unsuccessful attempt.
City insist they "absolutely refute" this version of events, stating that Al Mubarak provided no extra information.
Goal understands that City had held a long-term interest in signing Messi, although the new deal he signed with Barca in November 2017 put paid to their hopes of luring him to England.
Indeed there are fresh reports that Messi is in line for yet another contract extension.
Barca are confident that they can tie him down for the remainder of his career, with club president Josep Maria Bartomeu telling the Times recently: “He doesn't want to leave.
“We always tell him he can be a one-club man. That is his project too.”