The Ivorian was substituted in the 19th minute of Sunday's crucial tie in the Premier League title race, picking up what appeared to be a groin injury after an attempted shot at goal.
Despite initial fears he could miss the rest of the season, City coach Manuel Pellegrini revealed on Tuesday that the diagnosis was not as bad as first thought.
"Maybe it’s not as bad as we thought at the beginning, but he needs at least 10 days or two weeks to recover," said the Chilean.
There was better news elsewhere in the City squad ahead of their clash with Sunderland on Wednesday, with Vincent Kompany and Sergio Aguero cleared for selection.
"Vincent is fine - he on the squad list for tomorrow and so is Sergio - we'll see tomorrow who starts," added Pellegrini.
Defeat at Anfield left City seven points adrift of leaders Liverpool with two games in hand, but Pellegrini is confident his side can address the deficit.
"We win our two postponed games and we're a point back," he insisted. "If you don’t believe we can do it, you can’t believe in anything.
