The Belgian has been out of action since City's 1-0 win over Leicester earlier this month with a hamstring problem, joining the likes of Sergio Aguero, Edin Dzeko and Stevan Jovetic on the treatment table.
However, following Friday's 3-1 win over West Brom at The Hawthorns, Pellegrini revealed Kompany could be in line to feature against Burnley.
"Vincent Kompany maybe could be fit, we will see [on Saturday]," he told reporters.
"Edin Dzeko and Aguero will not be fit. Jovetic was on the bench today so maybe he will be fit for Sunday."
Asked for his views on City's routine victory in the West Midlands, Pellegrini expressed his satisfaction at keeping pace with Premier League leaders Chelsea despite the wintry conditions.
A first-half collapse from the hosts allowed City a 3-0 lead at the interval, with Brown Ideye's late goal proving only a consolation for Alan Irvine's men.
"[I am] very satisfied because we have three points more and because it was a difficult game," the Chilean explained.
"It's always difficult to play West Brom at home because they defend very well but also because we scored three goals even without strikers. In the way we are playing we are doing very well.
"Scoring three goals without strikers is not easy. We are not thinking about Chelsea, we are just thinking about winning our games.
"The title never finishes in December so we are not thinking about any other team."
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