The manager of the champions has been impressed with the striker since arriving at Old Trafford and says he is a "world class" player who can improve even further
After moving from Arsenal, the Dutchman finished his first campaign with the Red Devils as the Premier League’s top scorer with 26 goals last season.
The striker has already opened his account for this season, netting twice in United’s 4-1 win over Swansea on Saturday but Moyes thinks there is still room for improvement.
"I hope he can get better," Moyes told reporters. "His goals at Swansea were top goals, those of a top goalscorer, and you can see the difference it makes."
Moyes also revealed he was impressed with Van Persie’s all-round game at the Liberty Stadium on Saturday, not purely his goalscoring.
"I’ve got to say at the moment, with the way I’ve seen him, world class is sometimes used quite loosely but I think it’d be hard not to put him in that category that’s for sure," he added.
"We’re talking about his goals, but at Swansea, when he got the ball into him, with his hold up play and how he brought people into the game, that was impressive as well.
"He has an all-round game and we want to keep supplying him and give him every opportunity to score.”
The United boss also feels there is a hunger about Van Persie and a great desire to win more trophies, after claiming the Premier League for the first time last term.
"I asked the players the other day how many medals had they won. [Ryan] Giggs had won 13, quite a few of them had won five or six and Robin said he’d only won one," he added.
"So for me, the challenge is for Robin to keep trying to win medals and I think he’s got it, I think he’s driven to do it."