Mourinho has already made it clear that Rooney, will not play in a deep-lying midfield position like he did under former United boss, Louis van Gaal and former England manager, Roy Hodgson.
With the arrivals of Zlatan Ibrahimovic and Henrikh Mhkitaryan, as well as competition from Anthony Martial and Marcus Rashford, Rooney says he must fight for his place.
“I think you always feel pressure when you play for Manchester United,” he said.
“It’s one of the biggest – if not the biggest – clubs in the world and it’s been a pleasure and a privilege to play for them for so long.
“You always feel you have to prove yourself every season, because it’s a dream to play for them.
“I’ve only had one day [training with Mourinho] since we came out, but it was a very good day, the training session.
“But I think you only have to look at the teams he’s had before, and the success he’s had with them, and we’re hoping he can bring that to us.
“I’m excited for it. It’s a big season for us. The appointment of Jose Mourinho is a big appointment for us and we’re all excited by it. We’ve made some fantastic signings too.
“Hopefully we can have a good start to the season and be successful by the end of it.”