Carrick made 464 appearances for United across a 12-year spell and had a three-game stint as caretaker manager at the club in 2021, winning two games and drawing one.
The 44-year-old managed Middlesbrough between 2002 and 2005.
“Michael’s great fun. He is a great character, but don’t be fooled by how calm he looks,” Rooney said.
“He can have fun as well, but make no mistake, he’d be going in there now with full focus.”
Manchester United sit seventh in the Premier League after winning just one of their past six games.
Carrick’s first assignment comes on Saturday (12:30 GMT) when Manchester City make the short trip to Old Trafford.
“It is a massive game for the club, for Michael,” Rooney said.
“I think what he will do is bring a bit of calmness, a bit of grit to the game, which I think is needed. It is going to be very difficult, Manchester City are obviously a top team and it will be difficult to get anything out of it even at Old Trafford.
“But as we’ve seen over the years, Manchester United if they do turn up can win the game and hopefully that happens on Saturday.”