Jovetic, a £22million signing from Fiorentina last summer, has almost become City's forgotten man due to a catalogue of injuries and illness.
The Montenegro international has made just three starts - five appearances in total - and scored only twice for his new club.
Fellow strikers Sergio Aguero, Alvaro Negredo and Edin Dzeko have excelled without him, scoring 58 goals between them this season. Negredo was also signed last summer and club's other two other two major arrivals, Fernandinho and Jesus Navas, have also made an impact.
Yet while Jovetic is so far the odd man out in those groups, he has had little luck and Pellegrini hopes that soon begins to change.
The 24-year-old is close to fitness and could get an opportunity as City, with a 6-0 aggregate lead, travel to West Ham for the second leg of their Capital One Cup semi-final.
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."
Midfielder Jack Rodwell, another player hampered by injuries this season, is also hoping to feature at Upton Park.
Rodwell has made just three appearances this season after more of the hamstring problems that have blighted his career.
With such a commanding first-leg advantage, City's place in the Wembley final on March 2 is all but guaranteed.
Pellegrini is expected to make a number of changes with the likes of Costel Pantilimon, Micah Richards, Joleon Lescott and James Milner among those who could be involved, along with youngsters Marcos Lopes and Emyr Huws.