It is no secret that Rooney endured a significant dip in form, at least in the goalscoring department, netting only eight league goals last season.
During a 12 year spell at the Red Devils Rooney has never ended a season with less goals and the club have just added Zlatan Ibrahimovic to their books.
"I think you always feel pressure when you play for Manchester United," Rooney told reporters.
"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 United for so long.
"You always feel you have to prove yourself every season, because it's a dream to play for such a big club."
Rooney is also certain that Mourinho can help take the club back to the top where he feels they belong.
"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," said the 30-year-old said.
"The appointment of 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."