The Belgian centre-back has not featured for City since a 3-1 victory over Everton on October 5, when he picked up a thigh problem.
And manager Pellegrini revealed his captain is still two weeks away from a return to action, ruling him out until after the international break.
"Of course we are concerned about that and we are trying to do all the best to see how we can improve in that sense," the Chilean told reporters.
"He has two weeks more. We hope if he continues the same way he will not have any problems."
But the City boss refuted reports that Belgium head coach Marc Wilmots was set to send his own physio to the UK to assess Kompany's condition.
"I don't know about that," he added.
Wilmots had earlier stated: "Our physio, Lieven Maesschalck, will travel to Manchester on Friday to discuss the rehab programme with City's doctors and Vincent.
"We only play two friendlies, so it's good for him to have a good rest and that he recovers well to be on top with City again."
Manchester City face Sunderland in the Premier League on Sunday.