The Spain international was taken off on a stretcher with his right leg in a brace following an innocuous challenge with Billy Jones in City's 3-1 win over West Brom on Monday.
City now lie a point behind Chelsea and six adrift of leaders Liverpool, with a game in hand on both, but face an anxious wait to discover whether Silva will be able to feature again this season.
Pellegrini revealed the attacking midfielder had been playing with an ankle injury in recent weeks.
"Silva has a problem with his ankle. We'll see how he is (on Tuesday)," Pellegrini told Sky Sports.
"He has played the last three games with an ankle problem.
"The problem with David is he played the last game with that pain. I don't know if that pain increased or if he has a new problem."
Pellegrini was delighted to see his side return to winning ways against West Brom after dropping points against Liverpool and Sunderland.
City were not always at their fluent best on Monday, but were able to triumph with a degree of comfort as Argentinians Pablo Zabaleta, Sergio Aguero and Martin Demichelis found the net.
"I think we played a very good first 45 minutes. Maybe the goal they scored made us a bit nervous and in the second half we were not so clear with the ball," added Pellegrini.
"We keep the result and that is the most important thing.
"(The table is) exactly the same thing but we have three points more. If Liverpool win three games and 14 in a row they will be the champions.
"Our duty is to try win our games and in that way Liverpool can feel the pressure.
"We have to do our work and our work is to win our games."
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
