The 28-year-old has had a tough time ever since he took on the responsibility of captaining both his club and country.
In recent games at domestic and international level Rooney has looked lethargic and ineffective, which has led many questioning whether the Evertonian is already past his best.
However Moyes, who was sacked by United in April, has backed his former striker to thrive in the new roles that he has been given.
The Scot told The Sun: "He has proved he is a top player, now he will want to show he can take on the responsibility and be a top captain."
"He may be taking the armband at a difficult time, everyone knows Manchester United are going through a transitional period. I don't think the responsibility will weigh him down but instead help him kick on."
Rooney was one of the few players who thrived under Moyes' stewardship last season. He scored 17 goals and made 10 assists in 27 Premier League games, which is his third highest goal return for United in the league.
Moyes rejects claims that Rooney has hit his peak too soon and believes there isn't anyone who can take his position in both the England and United squad.
He added: "Some people might wonder if we have seen the best of him. I don't. I still believe he is one of the best in the Premier League."
"There will always be young players pushing hard for his place but right now I don't believe there is anyone who can dislodge him for club and country."
"What he needs to make sure is that he's not trying to do everyone else's job too. Sometimes he feels like he has to do everything."
The failed ex-United manager might feel Rooney needs to stop trying to do everyone else's job, but in recent performances he has barely dropped deep to help out his team-mates and has looked poor.
As a total striker he lacks that burst of pace which used to see him run behind the defensive lines to create space and chances, and with age he is only going to get slower.
Whether Rooney or any of his managers like it or not, his days as a striker are numbered. Eventually you would expect the number 10 to find himself deployed as a central midfielder where he will get much more of the ball and his fading abilities won't be so exposed.