There have been suggestions that the 30-year-old striker is struggling to adapt to the new manager's training methods, and is not convinced that he is the right man to replace Sir Alex Ferguson - the key man behind the Dutchman's transfer to Old Trafford.
However, the Old Trafford star insists he is a fan of the former Everton boss' tactics, and revealed that the 50-year-old's approach has brought a "very good atmosphere" to the club.
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"We have worked very hard from the day we started our tour to Asia and Australia. This will result in good matches, that's for sure. There is a very good atmosphere at the club.
"I'm happy with the style of Moyes. He does his own training sessions, he's close with the players and, with his staff, prepares us very well for the next opponent. That keeps us in shape. Luckily, winning the title last year gave us hunger for more."
Van Persie scored twice in a 4-1 win against Swansea on the opening day of the 2013-14 season, but struggled in the 0-0 draw with Chelsea and was in danger of being dismissed in the 1-0 defeat to Liverpool after a confrontation with Steven Gerrard.
Moyes has endured a challenging start to life at Old Trafford - a difficult fixture list has only yielded four points from three games, and the club is set to hold an internal inquest into a disappointing summer transfer window with Marouane Fellaini the only big-name signing on a farcical deadline day.