Rice, who was born in London, has been omitted from Martin O'Neill's Republic squad for their next two games as he considers switching his allegiance to the country of his birth.
"His heart must decide if he feels more Irish or more English," Pellegrini told BBC Sport. "With England he will have big competition but I think he is able to take that challenge.
"Maybe for him it can be more easy to play for Ireland but if you trust in yourself and you feel that you are an English player. It is a personal decision.
"It is very difficult to give advice but I am always speaking with him because he is young. When you are 19, you need to be strong - he is a strong player, he is a good technical player. I think he has a big future."
Ireland face Wales in their opening UEFA Nations League game on September 6 before a friendly against Poland five days later.