The center back has been out of action since Oct. 5 but is back in contention for the trip to the Hawthorns as Manchester City aims to correct its poor away form.
Kompany has been out of action since suffering a thigh injury during the first half of City's 3-1 win over Everton on Oct. 5, with further setbacks resulting in a lengthier spell on the sidelines than initially anticipated.
In stark contrast to its dominant home form, City has picked up just one league win away from the Etihad so far this season, meaning Kompany's presence could be a huge boost for Pellegrini ahead of the trip to the Hawthorns.
"We'll see [if Kompany is available]," Pellegrini said after Sunday's 3-0 win against Swansea. "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 its travel woes in the upcoming away games, 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 [the away games] if we want to continue fighting for the Premier League."