Either Michael Carrick or Ole Gunnar Solskjaer is set to be named manager by United to the end of the season after last week's dismissal of Ruben Amorim.
Former United captain Rooney said on his personal podcast: "Whether Michael goes in or if that's Fletch (Darren Fletcher) or John O'Shea or myself, it needs people who know the football club.
"Roy Keane - I know Roy has had his opinions, I said about Roy going in earlier in the season. Having people who know the club, who care for the club and understand what it takes to be a Manchester United player - that's where the club needs to be.
"The club has lost its identity, it's lost that family feel, if you like. Whether it's Ole (Ole Gunnar Solskjaer) or Michael, this is an opportunity to bring that back, bring the spirit of Manchester United back to the football club.
Asked about joining the coaching staff, he said: "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."