Roy Hodgson’s men travel to world champions Germany next weekend for a mouth-watering friendly that is followed up days later by Holland arriving at Wembley.
However, the 24-man squad named on Thursday for those matches looks set to change after Sterling and Hart were injured as City lost 1-0 at home to rivals Manchester United on Sunday.
Sterling pulled up with a groin complaint midway through the first half and Hart was taken off on a stretcher after half-time, having sustained a calf injury trying to clear up a terrible Martin Demichelis backpass.
“Both of them have muscle injuries,” City boss Pellegrini said. “Raheem his groin and Joe in his calf.
“I don’t think that a muscle injury you can be fit in one week. Normally three or four weeks.”
Hart and Sterling join the likes of Wayne Rooney, Jack Wilshere and Luke Shaw on the sidelines.