United last took the title in 2013, Sir Alex Ferguson's final season. Since then David Moyes, Louis van Gaal and Jose Mourinho have failed to emulate the Scot but Solskjaer has guided them to the top of the table, where they are two points clear of Manchester City.
"It's the first time in a few years where you can see Manchester United feel they can win this league and I believe they can," said Rooney, who was made permanent boss of Championship strugglers Derby last week.
"Six weeks ago I said to the coaches in the office here that I felt United would win the league - I still feel that today. When I watch them they excite me.
"The players with winning mentalities will relieve a bit of the pressure on Paul so he can show his quality on the pitch.
"They've got very talented players and they have a very good game plan going into games. I thought they deserved to beat Liverpool at Anfield recently.
"With a little bit more care with the final pass, Marcus Rashford would have been clean through two or three times."