Carrick secured Champions League football last Sunday but has yet to be told whether he has done enough to land the job on a permanent basis.
United have yet to make a call on their manager even though Carrick is the firm favourite not just amongst fans but also top players such as Bruno Fernandes to take the job permanently.
The former midfielder was appointed interim boss in January after Ruben Amorim's explosive press conference following the draw at Leeds and has since completely turned the club around.
As the club decide on who will take the job, Rooney spoke on Match of the Day about how delaying decision may actually harm the club.
"Manchester United need to invest in players in the summer in order to compete in the Premier League next season, in the Champions League next season, which is where they want to be. They have to invest. They have to strengthen the squad and I don't think there's any denying that.
"Now, if I was a player and Man Utd wanted to sign me, the first question I'd ask 'who is the manager? Does the manager want me?' So I think for Man Utd to have clarity on the manager."
"I think for the club to announce him, I think they need to do it swiftly because they need to get players in. They need to get players to improve that team."
Carrick has won ten of his 15 matches in charge and a decision from the board should come in the next few months as he waits to see if he will guide the side into next season.