The 19-year-old is eligible to be selected by Aidy Boothroyd for the tournament, although he has already established himself as a regular member of the senior squad having won eight caps for the Three Lions.
Rashford has also made 44 appearances across all competitions for United this season, and Mourinho questioned the wisdom in asking him to drop back down a level for this summer's tournament.
"I don't want to go in that direction. I just feel that, when a player reaches a certain level, it doesn't make a lot of sense to drop levels," he told reporters.
"It's like me putting him in our Under-23s to win, let's say, a derby against Man City. No? Nicky Butt could play him in that game because of his age.
"So when you reach a certain level and you've reached it for a long time, I don't think it makes sense. But the power is in their hands."
Rashford has scored 10 goals for United across all competitions this season.