The 19-year-old was once again left out of the Republic of Ireland squad on Thursday as he debates switching allegiance to England, the country of his birth.
Rice's decision to step back and think long and hard about his future has not sat well with some, but Pellegrini says people need to be patient and allow the youngster to come to his own decision.
"I am always talking with all the players, Declan also," the chilean explained.
"He is a young player and we need to give him time to make a difficult decision. We must not pressure him about which country he will play for. He needs time.
"He can be a top player. He is learning a lot and always listening and asking what he can improve. He is very young but has a huge future."