The 29-year-old has just one year left on his current contract at Stamford Bridge, and now looks set to depart.
According to the The Athletic, the player is understood to be keen on joining the Premier League champions.
The report adds discussions remain ongoing between the two clubs as they look to find a solution.
Pep Guardiola is a huge fan of the Croatia international, having kept a close eye on the midfielder during his time at Real Madrid.
Kovacic joined Chelsea in 2019 from Los Blancos initially on loan, before inking a permanent five-year contract.
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He has made 142 Premier League appearances so far, featuring 37 times in Chelsea's recent campaign, but made just 17 starts this season.
During his time at Stamford Bridge, Kovacic has won the Champions League and Europa League, as well as a UEFA Super Cup and FIFA Club World Cup.
Kovacic has previously earned praise from current teammate Kai Havertz, who looks set to join Arsenal this summer.
The Germany international, when asked who is the most skilful at Chelsea, said: "The best technically is Mateo Kovacic," adding "I suppose he doesn't use many skills in-game. That is Joao Felix, I'd say. Hakim Ziyech is the one who always tries to nutmeg."
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Guardiola is keen on a new midfielder with Ilkay Gundogan set to leave the club during the summer transfer window.
The 33-year-old was named on Man City's released list, and is yet to pen new terms with the treble winners.
Kalvin Phillips' future at the club is also in doubt, having failed to nail down a place in Guardiola's starting XI, since signing from Leeds United.
The 27-year-old netted his first England goal as England thrashed North Macedonia 7-0 at Old Trafford in their latest Euro 2024 qualifier.
Kovacic is seen as an alternative to Declan Rice who looks set to join Arsenal in what would be a club-record fee for the Gunners.
Man City were keen on the West Ham skipper, but as of yet, have not submitted any formal bid for the England international.