Manchester United staged a late bid for the Montenegrin international but the report claims Pellegrini is on the cusp of completing the deal after "intensive" talks between the player's representatives and City sporting director Txiki Begiristain on Wednesday.
Jovetic's agent, Fali Ramadani, reportedly held discussions with City officials, who green-lighted a five-year contract with £80,000-per-week.
Fiorentina had given City permission earlier in the week to talk numbers with their star striker.
It comes after United reportedly attempted to muscle in on the action. The report claims they still haven't given up hope entirely, but it looks increasingly likely that Jovetic will not be heading to Old Trafford.
Chelsea, Arsenal and Juventus have all been linked with the young forward as well. But they have all moved on to other targets, leaving the Manchester giants in a straight fight.
Ramadani has informed City that he wants to hold a final round of talks with both Manchester clubs before his player makes a final decision, but it's believed City are in pole position.
They hold the advantage of an existing relationship with Fiorentina, having swapped Stefan Savic plus cash for Matija Nastasic last summer.
Jovetic would be a key piece of Manuel Pellegrini's plans next season as he pledges to play an exciting attacking style of football at the Etihad Stadium.
The 23-year-old was Fiorentina's top scorer last season, bagging 13 goals from 31 Serie 'A' appearances. He can play in any of the three attacking midfield positions - through the middle or out wide - or can operate as a striker.