United parted company with Jose Mourinho after two-and-half years this week, with Ole Gunnar Solskjaer faring well in his first game in interim charge.
Rooney was a pundit for the 5-1 victory over Cardiff, and implored his former club to appoint someone in the mould of Liverpool manager Klopp – “a dream to work for”.
“I think Jurgen Klopp looks like a dream to work for and we’re talking about Manchester United – that’s a manager that Manchester United need to get in, that style and that philosophy,” he told BT Sport.
“From the outside all the players love him, all the fans love him. You want to go and play and win because it means so much to him.”
On Mourinho’s apparent surprise sacking, the former club captain added: “Something had to change and it was the right decision.
“To be a successful football club, you need everything to be right, to be happy.
“That rubs off on the players. The relationships between some of the staff and the players wasn’t great.
“But the players are smiling again. It’s a good move for the club, and it’ll be fascinating to see how Ole sets the team up and how they play today.”
After a game in which United scored more than four goals in a Premier League match for the first time since Alex Ferguson’s last in charge in 2013, Rooney added: “Everyone from the staff to the kitmen, they weren’t enjoying it. You can see the staff are happy today and the players are too.
“The lads played with a lot of energy, enjoyment and excitement.
“When you’ve got confidence, you put yourselves in positions to score goals. That’s what we did. We were playing higher and the full-backs were higher. We pinned them back and created a lot of chances.”