Kompany is nearing the end of his recovery from a groin injury, while Silva is suffering from a thigh problem, but Pellegrini is hopeful that both can be included against Manchester United next weekend.
The 59-year-old told reporters: "Kompany is okay, but I think it is a big risk for him to play three matches in one week. He needs two or three more days to be 100%.
"We will see next week what happened with Silva. We hope he can be, not sure – we will try for the derby."
The former Malaga boss has seen his new side earn six points from their first three Premier League matches.