The 31-year-old Argentina international has been repeatedly linked with a move to the Etihad since Pep Guardiola was appointed manager in the summer of 2016.
And club chairman Khaldoon al Mubarak has been quoted in a Spanish newspaper as saying he once made a lucrative offer for Messi, which was rejected.
'We asked Guardiola to talk to him, we offered him triple the salary he has at Barcelona, but he never accepted,' Mubarak was reported as saying.
However, City have told Press Association Sport the reports are untrue.
'We deny the veracity of these quotes,' a City spokesman said.
Messi played under Guardiola for four seasons at Barca, during which time they won 14 titles including two Champions League trophies.
So far this campaign Messi has scored eleven goals in as many appearances for Barcelona across all competitions, while he has provided five assists.
Messi's current contract at Barcelona runs until the summer of 2021.
Daily Mail