City beat Crystal Palace 3-0 on Saturday with midfielders David Silva and James Milner operating in central roles in the absence of Sergio Aguero, Stevan Jovetic and Edin Dzeko.
Montenegro international Jovetic is the closest of the trio to being fit after a hamstring injury but has been ruled out of the game at The Hawthorns.
Captain Vincent Kompany, the influential Belgium defender, also remains on the casualty list but is close to a return.
Manchester City injury list
Manchester City injury list
1/6 Vincent Kompany (defence)
The City captain suffered a groin injury during the Manchester derby defeat and was forced off at half-time. Kompany could miss the rest of the season.
2/6 James Milner (midfield)
James Milner is suffering from a knee injury that also forced him off in the loss to United, and will miss the match against West Ham.
3/6 Stevan Jovetic (striker)
Stevan Jovetic has not played for City since the 3-0 win over West Brom on 21 March after suffering a muscular injury
4/6 Gael Clichy (defence)
Gael Clichy lasted the full 90 minutes against United but has been ruled out of the West Ham game with a muscular injury
5/6 Wilfried Bony (striker)
The £27m January signing has no played since suffering an ankle injury in training after the West Brom game in March
Dedryck Boyata is in contention to return against West Ham
Pellegrini said: "The injuries are the same as last week. The strikers - Sergio, Edin Dzeko and Jovetic, and Vincent Kompany.
"I am not a doctor so it is difficult for me to know exactly but maybe Jovetic and Kompany will be soon, the end of this week or next week.
"Edin Dzeko and Sergio Aguero will be the second part of January."
After Friday's game at West Brom, City host Burnley on Sunday and then face Sunderland on New Year's Day.
There looks to be a possibility of Jovetic and Kompany featuring for part of that programme.
Pellegrini also confirmed that left-back Gael Clichy, who missed the Palace game after a minor knock, is fit.
Pellegrini is hopeful that discussions over the the future of on-loan midfielder Frank Lampard will reach a positive conclusion soon.
The former England international's loan from sister club New York City is due to expire at the end of the season but Pellegrini has expressed hope the player can stay.
Lampard, 36, has also indicated an interest in staying longer, but it remains to be seen how long an extension can be secured given the start of the Major League Soccer season in March.
Lampard is a key figure in City's bold plan to make an impact in the United States but Pellegrini is hopeful a deal can be agreed that suits all parties.
Asked if he risked upsetting his American counterparts, Pellegrini said: "I don't think so. That is why we have long conversations with all of them.
"That is just one club so I think that what is better for the club is better for all the clubs.
"I hope Frank's situation will be resolved in the next days. I said in the beginning it will be during December we are going to have the last decision.
"I repeat, Frank is very important for our team so I hope he will stay here."
City head into the festive fixtures trailing Chelsea by three points at the top of the table.
The champions did pull level with their victory at the weekend but Chelsea responded to the challenge by winning their game in hand at Stoke on Monday.
City, with momentum after six successive league wins, will hope to keep up the pressure but Pellegrini insists he is not concerning himself with Chelsea's fortunes.
He said: "We are not thinking about Chelsea, we are thinking about just our team. We know it is important to have our own pressure.
"You never win the title in December. We have a long five months to continue playing as well as we are doing so far and we will see at the end of the season which team has most points."