The 29-year-old striker scored 30 goals in 48 appearances during his debut season with the Red Devils, after joining from Arsenal.
And Moyes, who succeeded Sir Alex Ferguson as United boss in May, has been impressed by what he has seen from the Dutch international since he joined up with the rest of the squad for their pre-season global tour.
"We've enjoyed him being here. He met up with us when we arrived in Sydney, he's trained quite a bit on his own," Moyes told a press conference.
"I'm really looking forward to seeing him start and get him playing again. He was a massively important player for Manchester United last season and (we're) hoping he'll have as big an influence again this season.
"I got to see him this week for the first time and I mean his control, his touch, his awareness, just in small games we've played this week," he added.
"I've really been impressed by his professionalism as well, the way he's gone about his work, he's trained hard this week."
Van Persie missed last weekend's 1-0 loss to Thailand's Singha All-Star XI in Bangkok and is expected to come off the bench during Saturday's game against the Australian A-League All Stars.
"What we are doing is trying to get him into a condition where he is ready to do exactly what he's done last season which was score goals for Manchester United and he was a really big influence in the team. So we're hoping to get more of that this season," added Moyes.
Meanwhile, midfielder Michael Carrick believes United will have to be at their very best to see off the challenge of their rivals and repeat last season's title triumph.
"With us and City and Chelsea changing managers there's a bit of a different feel about it but they all have got strong squads. The best teams come to the top and hopefully we'll be up there," said the England international.
"But it'll be tough as there's probably five or six teams now that fancy their chances of the title, or certainly the top two or three, so we'll have to be as good if not better than ever."