Hart has lost his place to Costel Pantilimon at City for the last three matches, following a string of errors in recent months.
Pellegrini reckons it is fitting that the 26-year-old is involved in Roy Hodgson's set-up after helping his country qualify for the World Cup.
"I am happy, absolutely - he deserves to be in the squad," Pellegrini said. "He has been the number one English goalkeeper for the whole of qualifying for the World Cup. I think he must be there."
But Hart is likely to remain on the bench as City travel to the Stadium of Light on Sunday to play struggling Sunderland.
"I am thinking about what is the best for the team at this moment," Pellegrini added. "At this moment, I repeat, I have trust in Pantilimon.
"But we will continue trusting in Joe and will see when he comes back."
Watch Sunderland take on Manchester City live on Sky Sports HD1 (2.05pm kick-off) during Ford Super Sunday.