Pep Guardiola's side have presented Napoli with a take-it-or-leave-it-offer. That's according to Il Mattino, who say that City have given the Naples club a final offer of €73m (£65m) including bonuses.
If the Italian side don't accept City's demands, they may move on to other targets - which previous reports suggest Napoli may not be able to afford.
Like most communications between the sides, it has reportedly been carried out through the player's agent, Fali Ramadani. He's been at the forefront of negotiations because of the poor relationship between the clubs.
Negotiations have dragged on for several months, creating one of the longest-running transfer sagas of the summer. In the last week, this has been overshadowed somewhat by Lionel Messi's unexpected links with City, but sources have reported over the last few days that a deal to bring Koulibaly to the Etihad is still very much in the works.
City's first game of the season is away to Wolves on Monday 21st September- and they're keen to bring in any new signings before then, despite the transfer deadline being extended until 6th October this season.
At 29, Koulibaly is Senegal captain and has established himself as a leading centre-back in world football.
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