Van Persie has been linked with a move away from United following rumours that he was unhappy with life under Moyes.
However, the Holland striker has dismissed such speculation, insisting in an interview published in United's match programme that he is content with the Premier League champions.
"The truth is I'm very happy here at this club," Van Persie said.
"I signed for four years and I'd be delighted to stay even longer, beyond the next two years I have left on my contract. This is how I feel, although it's not what has been suggested in the media."
When asked in his pre-match news conference ahead of the Super Sunday clash with Liverpool, Moyes welcomed Van Persie's remarks.
"It's nice of Robin (to say he is happy to stay)," he said. "He is happy here and we are very pleased about that.
"He has a couple of years to go on his contract and I am sure that (an extension) is something the board will look at."
Moyes believes the fixture with Liverpool is the biggest in the country, adding: "There has been great history between the two clubs over a long period. I think it's the biggest club game in the Premier League.
"To win would be a big boost. It would be an important three points."