Reports in the Spanish press has suggested that City made a £132m deal to buy out the remainder of Messi’s contract with Barca.
City were also supposed to be ready to pay the 21-year-old €10million a year.
City has been linked with several star players since being taken over by the Abu Dhabi United Group last summer.
“Manchester City Football Club note with interest the reports circulating in the Spanish media that the club have made an offer to the Barcelona player Lionel Messi and that he has turned down the chance to join the club,” read a statement.
“While acknowledging that Lionel Messi is a world-class player of the highest calibre, Manchester City would like to make it clear that the club has at no time made an approach to Mr Messi or his representatives.”