After months of speculation, Van Persie broke his silence on speculation regarding his future on Thursday night.
The Manchester United forward scotched rumours he wanted to leave Old Trafford and denied reports that he does not approve of Moyes' training methods.
The former Arsenal striker said he was so happy at Old Trafford that he was willing to sign a new contract beyond 2016 and Moyes thinks the United hierarchy will be interested in extending the 30-year-old's current deal.
"It's nice of Robin (to say he is happy to stay)," the United manager said.
"I've been telling you that [that he's staying] but you've wanted to say or write something different to what I've been saying.
"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."
As Moyes admitted himself in an address to fans last week, he never expected his debut season as United boss to go as badly as it has done. Ahead of Sunday's huge game against Liverpool, Moyes' men sit sixth in the Barclays Premier League table, some nine points off the top four.
But a dreadful performance against Olympiacos aside, Moyes can look back at the past fortnight and say he has scored two significant victories.
Van Persie's public declaration that he is "very happy" at Old Trafford came just a few weeks after Wayne Rooney also committed his future to the club by signing a new five-year deal worth £300,000 a week.
United have lost just three games when Rooney and Van Persie have started together, so no wonder Moyes is happy to have both players' futures resolved.
"I've always said I think we've got two outstanding forwards in Wayne and Robin," Moyes said.
"Both have capabilities of winning games off their own back. They're both pivotal international players.
"They're 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 showing that they both want to be Manchester United players."
With Van Persie and Rooney now committed to the club, Moyes' focus shifts to potential incomings.
Moyes has been promised funds to buy four big-name signings this summer, with a left-back and a central midfielder at the top of the Scot's wish list. Southampton's Luke Shaw and William Carvalho of Sporting Lisbon have been strongly linked with the Old Trafford club.
Both could play for England and Portugal respectively at this summer's World Cup, where a player's valuation can rocket if they put in a series of outstanding performances.
Moyes is conscious of that and he therefore hopes to get most of United's transfer business concluded before the tournament begins.
"Yes, I might do," Moyes said when asked if he would prefer to complete any deals before the World Cup starts on June 12.
"Obviously we are getting ourselves prepared now as well as we can.
"You can't do an awful lot until the end of the season really but we will try and be prepared as much as we possibly can. You don't always get all your ducks in a row but we will try and get as many of them as we can."