The Croatia international is out of contract next year and Chelsea are actively looking to offload players who have 12 months remaining on their deal instead of seeing them leave on a free transfer next summer.
City were given permission by Chelsea to hold talks with Kovacic last week over a move in the upcoming transfer window.
And according to Fabrizio Romano, the Premier League champions have now agreed a contract with the Chelsea midfielder.
City will now continue negotiations with Chelsea over a fee for Kovacic, who was signed in a £40 million deal from Real Madrid in 2019.
Kovacic is not the only midfielder leaving Stamford Bridge this summer as N’Golo Kante is also set to depart after seven years at the club.
Kante, who struggled with injuries this season and made just nine appearances in all competitions, will leave Chelsea on a free transfer once his contract expires.
Elsewhere, AC Milan are continuing their push to sign Ruben Loftus-Cheek, who is keen on a move to Italy.
Manchester United also remain in talks with Chelsea over a fee for Mason Mount after their £50m bid was submitted this week.
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