Kompany has been out of action since suffering a thigh injury during the first half of City's 3-1 win over Everton on October 5, with further setbacks resulting in a lengthier spell on the sidelines than initially anticipated.
Fitness problems have occurred with worrying frequency for the Belgium centre-back, who was regularly troubled by a calf complaint last term before being ruled out for a month by a groin injury sustained during this season's opener versus Newcastle United.
Although City maintained their 100 per cent home league record with a 3-0 win over Swansea City on Sunday - a third consecutive clean sheet on their own patch in the Premier League – Martin Demichelis and Joleon Lescott endured some rocky moments at the heart of Pellegrini's defence, as had been the case during Wednesday's 4-2 UEFA Champions League triumph over Viktoria Plzen.
In stark contrast to their swashbuckling home form, City only have one league win on the road so far this term , meaning Kompany's presence would be a huge boost for the trip to The Hawthorns and Saturday's visit to Southampton.
"(On Monday) we'll see," Pellegrini said after the Swansea match.
"He worked normally for the last three days with the whole squad.
"I think maybe he will be fit on Wednesday."
After scoring a second-half brace, Samir Nasri spoke of the importance of City finding a cure to their travel woes in the upcoming away matches and Pellegrini echoed his in-form playmaker's sentiments.
"It's a big challenge because they are a strong team playing at home," he said of West Brom.
"We've finished this week playing three games at home. We hope that now we can start winning away because, I repeat, we deserved to win some of the games that we lost.
"But in this week we have six points. We must try and win all of them (away games) if we want to continue fighting for the Premier League."
