The Daily Star says Pellegrini is considering giving Hart back his Premier League starting spot for the first time since October 27.
Pellegrini ditched the England No.1 after he handed Chelsea their winning goal in a 2-1 defeat and following a string of other costly errors.
Romanian Costel Pantilimon has stepped up and played in City's last six league games.
Hart has been restricted to just two Champions League outings since being ousted by Pantilimon.
But Pellegrini still sees Hart, 26, as his long-term first choice at the Etihad Stadium.