The 29-year-old is now in advanced talks over a switch to the Etihad Stadium for £25million rising to £30m with add-ons.
Kovacic has already agreed personal terms with City, having not been offered a contract by Chelsea and with just a year left to run on his deal at Stamford Bridge.
The Croatia international is now expected to leave Chelsea after winning the Club World Cup, Champions League and Europa League during five years at the club.
Kovacic has played 221 times for Chelsea, who hope to sign Brighton’s Moises Caicedo as his replacement.
The Ecuador international is keen to move to Stamford Bridge but Brighton will demand a significant fee for him.
It remains to be seen whether Chelsea can agree on terms after having a £60m bid rejected a fortnight ago.
They will not entertain the idea of a swap deal including defender Levi Colwill.
Southampton’s Romeo Lavia and Everton’s Amadou Onana have been sounded out as potential alternative options.