Mourinho said: "Knowing that probably it is Michael Carrick's last year, the people that are behind him, they have to prepare themselves for that."
So can that new leader be 24-year-old France midfielder Paul Pogba?
"I would say he is the leader of the young guys," said Mourinho. "He is probably the oldest of the young guys.
"He has big experience at such a young age, at the same time he's still the kid that come from the academy, the way he is in the club, the way he is in the group, in the training ground.
"He is still that kid from the academy but with his experience, with his status and with his quality on the pitch, where he is also a key player for us, I think Paul has conditions to be in a couple of years such an important guy in the club."
Pogba, who rejoined United for a world record £89m in 2016, added: "I came here to hopefully be a leader. That is how it should be.
"I want to grow up as a leader and a player as well. I can learn from the older players and become a leader."