"I do think we'll be challenging this season -- we've still got that belief and it is even stronger after working with this manager and the players over the last few months," Rooney told British media.
After suffering back-to-back defeats last month, a five-game unbeaten run in all competitions has raised spirits as seventh-placed United held rivals Liverpool to a 0-0 draw on Monday to maintain a five-point gap behind leaders Manchester City.
"I think we've got a fantastic squad that is ready and capable of challenging. I'm sure over the next few weeks or couple of months we will have our way of playing, and it will be his (Mourinho's) way of playing.
"It is a different way of playing, but if you're an individual you should learn what the manager wants. As a team, it's going to take a little bit longer. We knew it was going to take a bit of time," Rooney added.
Following his world record move to United in August, midfielder Paul Pogba has yet to live up to his hefty price tag but Rooney is confident that once the Frenchman adapts to the rigours of English football, he will be well worth the outlay.
"Paul is a fantastic player, I think he is working hard and he is doing well," the England international added of the former Juventus star.
"It is a different league to what he's been used to -- he didn't really play last time when he was here so this is all new. He is a fantastic player and he will shine for us this season there is no doubt."
United host Turkish side Fenerbahce in the Europa League on Thursday before travelling to face Mourinho's former club Chelsea in the Premier League on Sunday.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by John O'Brien)
