"Samuel Eto'o is undoubtedly a fine footballer but the circumstances surrounding him were such that the deal could not be completed," City chief executive Garry Cook told the club website.
"We now feel the time is right to pursue other avenues and we have a clear and strategic transfer plan, which we continue to follow."
City manager Mark Hughes confirmed last week that a 25 million-euro ($34.85 million) bid had been made for the Barcelona striker and had warned the forward that he would not wait all summer for a decision.
Any possible deal had been delayed while the Cameroon international considered his future after also being offered a new two-year contract by the Spanish and European champions.
Eto'o finished last season as Barca's top scorer with 30 league goals in coach Pep Guardiola's first year in charge.