The Red Devils legend, who is the club's all time leading goalscorer with 253 goals in 559 appearances, has thrown his support behind his former teammate.
Carrick took over from Ruben Amorim in January, and on Sunday (04.05.26) he secured a return to Champions League football with a special 3-2 win over Liverpool to strengthen his own chances of landing the United job on a permanent basis.
Speaking on BBC's The Wayne Rooney Show, Rooney said: "Michael Carrick is a clever person, he's a really good coach, and I think he can lead the team for however long he wants if he gets it right.
"It will be an interesting summer. For the first time in a long time Manchester United seem like they have a bit of calmness around the whole place and that's a good thing."
Since Carrick returned to the Old Trafford dugout on January 17, his United team has picked up more points than any other Premier League club.
After such a successful stint, Rooney has suggested Carrick's appointment is only a matter of time.
He said: "It's when rather than if I think. In my opinion it wouldn't be a bad decision.
"The one thing we're hearing is that there's Champions League football next season and more games so how is he going to deal with that.
"He's been in the Championship with Middlesbrough where squad rotation is actually even more difficult than it is in the Premier League because normally you've got about 14 players with a bit of quality and the rest beyond that haven't.
"He's been there, he knows how to do that. If you brought in a Luis Enrique or Thomas Tuchel and they won 10 of of their first 14 games you would say that's incredible.
"So, just because he's a young, English manager it means it's not the right place to look in a lot of people's eyes."
After Sunday's win, Carrick - who has won 10 out of his 14 games this year - played coy about his future but outlined his credentials.
He said: "It's been a good run. We've beaten some very good teams and it's been challenging.
"I love doing what I'm doing. It's a great position for me to be in and it feels pretty natural, if I'm totally honest.
"I'm not being blase because it's a difficult role, but it feels like I've been here a long time. I can understand what it brings and to be sitting in this position is a good position to be in."
