The 27-year-old was one of two players, including team-mate Fernandinho, who suffered injuries during their club’s 5-2 win over CSKA Moscow in the Champions League on Tuesday.
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"Obviously we have another day before we make any decisions but David Silva, Richard Wright, Stevan Jovetic and Vincent Kompany will miss the Sunderland game," said Pellegrini at a press conference.
"As I say we have some more time but we will have to wait and see. Silva has a problem with his calf so he could miss three or four weeks."
However Fernandinho, who was replaced at half-time in the same game for James Milner, is expected to face a fitness test ahead of their weekend trip to Sunderland, along with central defender Matija Nastasic.
He continued: "Fernandinho and Matija Nastasic have slight problems but he could possibly be fit for Sunday."
Silva's absence could see him miss up to seven games including a league clash with Tottenham on 24 November and a visit to Bayern Munich in one of two Champions League ties.