Rooney was sacked by Plymouth on New Year's Eve in 2024 and has since stepped away from the touchline as well as coaching as he focuses on punditry.
Despite his absence, the former England star was asked on The Wayne Rooney Show if he would be interested in joining the coaching staff under Carrick, saying: “Of course I would. It’s a no-brainer.
“I’m not begging a job here by the way. Just so everyone knows, if I was asked to go in of course I would. Appointing the manager is the most important thing.”
The former striker has not called time on his management career and is open to a new role. Speaking to ComeOn, Stam believes Rooney could be a perfect fit for United heading into the new campaign.
“Wayne Rooney in a coaching role? I think it's good for a big club to bring in people with experience and quality who can talk about the game and help the players. If that opportunity is there, you need to take it.
“Nowadays in football, the staff is getting bigger and bigger because there's attention for everything. When we played, there were only two or three people walking around the pitch, and now there are so many more. But it's good because the intensity is getting higher.
“Football is much more detailed now. I think it's very important to instruct defenders, midfield players, or strikers individually. You can talk to them and give them certain tools that make it easier for them to play and become more effective in their style of play.
“If a person or former coach like that is available, and you can bring him in, and he's willing to help you out, then I think you need to take that opportunity.”
Carrick secured the Red Devils’ return to the Champions League last week with a win over Liverpool. The club may seek more help with coaching now they are back amongst Europe’s elite which may include a call to Rooney.