England play Germany in Berlin on Saturday and will face the Netherlands at Wembley on March 29.
City manager Manuel Pellegrini said both players might be out of action for three to four weeks.
"Both of them have muscle injuries," said Pellegrini. "Raheem (Sterling) is his groin while Joe is his calf - and I don't think muscle injuries are one week. Normally this is three or four weeks."
(Reporting by Aby Jose Koilparambil in Bengaluru)
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