The £27million BiH striker seemed certain to depart the Etihad this summer after falling out of favour with Roberto Mancini last season.
But Pellegrini has told the club that he believes Džeko can have a future at City. The 59-year-old is planning talks with the 6ft 4ins striker once he has been officially unveiled as Mancini’s successor this week.
And, if Džeko indicates that he is ready to fight for his place, the Chilean will keep him at the club.
Džeko did himself no favours last season with constant sulks, but his record of 40 goals in 109 games is impressive given that 47 of his appearances have been as a sub.
Pellegrini’s stance on Džeko has led to City’s interest in Edinson Cavani cooling in recent days.
Napoli will not accept anything less than the £52m buy-out clause that is in the Uruguayan’s contract and have not been receptive to the idea of accepting Džeko as a makeweight in any deal.