Rumours surfaced suggesting Van Persie had not been impressed by Moyes' reign so far after replacing Sir Alex Ferguson at the helm of the Premier League champions.
The Dutchman started this campaign well, netting both goals in United's Community Shield win over Wigan and another double in the comfortable opening-day triumph at Swansea - but he has not scored since.
Indeed, he has barely had a chance of note in the draw with Chelsea and defeat at Liverpool on Sunday, where his only opportunity came near the end, which he slid into the side-netting.
However the Dutchman, who is away on international duty with Holland, has moved to dispel the rumours and insists he is enjoying working under former Everton manager Moyes.
"It's great working with the new manager David Moyes," Van Persie is quoted as saying in De Telegraaf.
"He has his own style and methods and I like these.
"We are working 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 prepares us with his staff very well for the next opponent. That keeps us in shape.
"Luckily, because the title of last year gave us hunger for more."
Van Persie was United's big acquisition last year, but Moyes almost missed out on a star signing this time.
In the end United managed to recruit Belgium international Marouane Fellaini from Everton in the final minutes before the transfer window closed, bolstering their midfield options, but they missed out on targets including Leighton Baines, Ander Herrera, Cesc Fabregas, Sami Khedira and Fabio Coentrao.
So eager were United to land Fellaini that they ended up paying £27.5million - £4million more than if they had exercised an option in the player's contract which expired at the end of July.