It comes after the Englishman took over at Derby on a permanent basis earlier this year after initially being put in interim charge.
That saw the 35-year-old call time on his outstanding playing career and start life as a manager.
Rooney is fondly remembered by United fans who would no doubt love to see him in the Old Trafford dugout one day if he impresses as a coach.
He told the Mirror: “It’s hard to make any predictions because in the world’s top league, the manager is let go if they don’t get results.
“But I hope that Rooney will be successful and eventually become a manager at Manchester.
“He definitely has the personality, the experience and record for it.
“He’s the manager for Derby now, but I’m sure he’ll be creating success stories as a manager for a Premier League team soon.”
“He had the image of being mischievous and crazy, so I really didn’t know what he was like.
“But on the pitch, he fought harder than anyone and he protected his team-mates more than anyone.
“He was a team player. I played with many amazing football players at Manchester, but Wayne Rooney was the best athlete.”