Kolarov, who joined from Lazio in 2010, recently signed a three-year contract extension, while Jovetic looks set to become a more prominent figure in the new season after a frustrating debut campaign.
A host of Serie A clubs were reported to be chasing Kolarov’s signature, but the Serbia full-back says he is settled with City.
"I have extended my contract and I remain here," he told Sky Sport Italy.
"In the past I had been linked to Roma, Inter Milan and Juventus, and instead, I was one step away from another Italian team. Now I have no doubt about my stay."
Jovetic made a £22million switch from Fiorentina last summer, but made just 18 appearances in all competitions as injury problems and the fine form of fellow strikers Sergio Aguero, Alvaro Negredo and Edin Dzeko kept him out of Manuel Pellegrini’s side.
The 24-year-old has impressed during City’s pre-season preparations this summer, though, scoring twice in a 5-1 win over AC Milan and he has received Pellegrini’s backing ahead of the new campaign.
Inter Milan had been among the clubs linked with bringing Jovetic back to Italian football, but he is looking to show what he can do in the Premier League.
"Now I feel everyone’s confidence, so I’m staying here. Many of my friends from Italy called me, but I decided to stay here and prove who I am," he said.
"I’m fine there (at City), we will see in the future."