The Brazil-born Italy international was understood to be Pep Guardiola's chief midfield target and City had already agreed over a deal that would have seen the player move to Manchester. However, Chelsea have since swooped in to sign the player on a five-year contract.
The Etihad side are said to be furious over the recent proceedings but are now looking elsewhere in the hopes of beefing up their midfield ahead of the upcoming season.
According to the Daily Star, the Madrid and Croatia midfielder has emerged as a target. Kovacic, who only managed 10 league starts for Real last season, is unsatisfied with his role at the club and wants out.
Madrid, meanwhile, are willing to sell the player, but not for a fee below their valuation of £80m.
City only just signed Riyad Mahrez from Leicester City for a club-record £60m fee. And given their penchant for passing up on players who would have them exceed a certain budget, it will be interesting to see how this unfolds - if there's any truth to the story, that is.
Various outlets are also reporting that the club will sign Paris Saint-Germain wonderkid Claudio Gomes when he turns 18 later this month.
Gomes is rated as one of the best young players in France at the moment and he is expected to quit the Ligue 1 side to sign a five-year deal with the Premier League supremos this summer.