The Dutchman has been reportedly keen to leave the club in the summer and Goal understands that he clashed with the Scot earlier in the season and does have an exit clause in his contract should the club finish outside the top four.
However, Van Persie told the club's official website on Thursday that he is very happy with the team and the manager, sentiments that do not surprise Moyes.
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"It's difficult if you don't believe what I say. Robin is happy here and I'm pleased about that. I didn't know what was coming out - I've only just heard [on Friday] morning about it.
"We'll take it as it is. He has a couple of years to go on his contract and I'm sure that will be something the board look at.
"I've always said we've got two outstanding forwards in Wayne [Rooney] and Robin. Both have capabilities of winning games off their own back. They're both pivotal international players and the sort of players any side in the world would want in their team.
"I'm delighted to have both of them and, more importantly, that they both want to be Manchester United players."
Moyes also revealed that Nani is closing in on a return to action after a long lay-off, having returned to training.
"Nani is back. He had a really bad hamstring injury but he is back and has trained. Hopefully we get him up to speed very quickly," he added.
"Rafael, Javier Hernandez and Jonny Evans are all coming along. They all have a chance of playing on Sunday."