The Spaniard was taken off at half-time in Saturday's 2-1 win over Aston Villa.
Per the Mirror's David McDonnell, when asked if Silva would be fit for the trip to Anfield, manager Pep Guardiola said:
"I don't think so. I didn't speak with the doctor, but when he has a muscular problem and cannot play more minutes, it's because he has something.
"When it's a muscular problem, it's always a minimum of 10 to 12 days.
"Five minutes before the first half ended, he told me he had a muscular problem."
Silva, a key playmaker for the Sky Blues, has contributed two goals and four assists in the Premier League this season.
The Citizens will go into the game six points behind the Reds and in need of a win, so it's a blow not to have the 33-year-old's vision, intelligence and technical excellence in their side.
As football blogger Jordan-Luke McDonald observed, City will be without several players for their visit to Anfield:
The defending champions do have options to replace Silva, though, thanks to their strength in depth.
Guardiola could use the opportunity to show his faith in Phil Foden, whom he has singled out as Silva's replacement when his contract expires at the end of the season.
However, he has given the 19-year-old just three starts in all competitions this term, and two of them were in the Carabao Cup, so it seems unlikely he'll be called upon.
Bernardo Silva could be used in midfield instead, with Riyad Mahrez taking his place in the front three, or Guardiola could restore Nicolas Otamendi to the starting lineup and move makeshift centre-back Fernandinho back into midfield.
Either way, City can field a team who are more than capable of competing at Anfield, but it's far from ideal in such a crucial game.