Cook recalls the incident in Gary James's book The Manchester City Years, which charts the history of the Premier League champions.
Cook explains how on the final day of the summer transfer window in 2009, City approached Barca for the Argentina international by mistake, as club officials in Manchester, London and Abu Dhabi were trying to conduct business over the phone.
"An executive made a comment like, 'it's all getting messy'," he revealed.
"Via the phone lines and the other communication lines, this somehow translated into 'get Messi'.
"An offer was made for Lionel Messi of about £30m. Needless to say, it was rejected."
City subsequently went on to sign Robinho from Real Madrid for £32.5m on that day.