Jovetic, a £22million signing from Fiorentina last summer, has made just three starts - five appearances in total - and scored only twice for his new club.
The 24-year-old Montenegro international is finally close to fitness after a calf injury and could get an opportunity as City, with a 6-0 aggregate lead, travel to West Ham on Tuesday night for the second leg of their Capital One Cup semi-final.
Boss Pellegrini said: "It's an important chance for him to come back to play but I don't think he'll be able to play from the beginning or play 90 minutes.
"We'll talk with the doctor and if he doesn't have any risks, then maybe he will be in the squad.
"He came here to play in the Premier League. He was a very important player in Italy for Fiorentina and I still believe he will be a very important player for us.
"He can really start playing often in the next three months and I think he can be the player we hoped he would be."
Jovetic's City career stalled before it began as he suffered a hamstring injury during pre-season.
Since then, he has had further hamstring and calf problems while a potential appearance in the Capital One Cup quarter-final at Leicester was scuppered by illness.
Pellegrini, renowned for his man-management skills, concedes keeping Jovetic's spirits up has been one of his tasks.
He said: "It's very difficult to be happy when you're not playing and you have so many injuries, but he's conscious that he will (get to) be 100 per cent fit and demonstrate why he's here.
"We are trying every day to give him trust so that his bad luck will finish soon.
"It's very important that he comes back ambitious and hungry to be an important player here at Manchester City."
103 goals and our star signing hasn't even played yet. Whether we win anything this season or not, I just want to say how much fun it is supporting City these days...- frenchtony