Pep Guardiola has already identified the Croatia international as a signing to strengthen his midfield options and City have been working on a deal for several weeks.
Last season’s treble winners have agreed personal terms with Kovacic but are yet to reach an agreement with Chelsea over a transfer fee.
According to The Athletic, City have now submitted a £25m offer to Chelsea for the midfielder.
The report claims that Guardiola has also been a long-term admirer of Kovacic since his time at Real Madrid.
Kovacic, meanwhile, has just a year left on his contract and Chelsea are actively looking to sell players who have 12 months left to run in order to avoid seeing them leave Stamford Bridge on a free transfer next year.
The 29-year-old is set to be one of several players departing Chelsea this summer as the club looks to trim the size of Mauricio Pochettino’s inflated squad.
Manchester United are continuing their talks to sign Mason Mount, while Arsenal have tabled an improved offer for Kai Havertz.
Edouard Mendy has agreed personal terms with Al-Ahli, while Hakim Ziyech and Kalidou Koulibaly are also in talks to join the Saudi Pro League.
Inter have also explored the possibility of signing Koulibaly but want a loan deal for the defender, who cost Chelsea £34m last summer.
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