The Sun reports that only personal terms have to be finalised, with the 23-year-old set to sign a five-year deal worth £120,000-a-week.
New City boss Manuel Pellegrini is keen to bring in the Fiorentina ace to replace Carlos Tevez.
A source close to the Montenegro star told The Sun: “It’s pretty much sorted he’ll go to City.
“They just have to sort his contract. It shouldn’t be a big problem.”
Jovetic has also been strongly linked with the likes of Manchester United and Liverpool.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.