The Portuguese, who has 17 major trophies on his CV including eight league titles in four countries and two Champions League triumphs with different clubs, replaced Louis van Gaal this summer.
Rooney said Mourinho’s arrival has corrected that.
“It’s always great to get a new manager but when you get someone in the stature of Jose Mourinho he’s great to work under and he’s brought a winning mentality back to the club,” the England captain told Manchester radio station Key 103.
“Manchester United as a football club we have to win and we have to deliver for him.
“There’s pressure on the players but we’re ready and I think this season we’ll give a real challenge on all fronts.
“He’s come in, he’s been great with the players. The training has been hard but enjoyable.
“We’re ready, we’re working hard. We know it’s a big season for us.
“He’s made, in my opinion, some great signings who have gelled in really well with the squad so it’s exciting times.”
The 30-year-old starts the season needing just five goals to break United’s all-time scoring record held by Sir Bobby Charlton but he is already looking at life beyond his playing days.
“I’ve started taking my coaching badges now so that will probably take about four or five years to complete,” he added.
“Of course I’ve got a lot of experience playing football so I think it would be criminal If I didn’t try and pass that knowledge on so hopefully when I finish playing I can get some role as a manager or coach and try and use the experience I’ve built up over the years.”