The Red Devils reclaimed the Premier League title in 2012/13 - Van Persie's first season at Old Trafford following a big-money switch from Arsenal.
Domestic success justified the Dutchman's decision to leave the Gunners in search of major silverware, but he is determined to ensure that there are more medals to follow.
It has been a summer of change at United - with David Moyes having succeeded legendary boss Sir Alex Ferguson - but the desire to be the best remains and Van Persie says the Red Devils will be looking to challenge on multiple fronts in the upcoming campaign.
He said in The Sun: "I still have more years left and it's not like I'm saying, 'Yes, we won the league so that's me done'. I want more now. It makes me hungrier.
"I was hungry last year but now I'm more hungry. We have a great bunch of players so we can win more and do better.
"Last season we won the league and that was great but this time we want to win the league and more as well."
While United will enter the new season in optimistic mood, Van Persie acknowledges that they will need to raise their game again if they are to stay ahead of Chelsea - who have Jose Mourinho back at the helm - and neighbours Manchester City - who have spent big this summer under new coach Manuel Pellegrini.
He added: "Of course, we must improve to stay ahead of them as over the last few years the Premier League has become better. Every team has got harder to beat.
"When going away you must perform 100 per cent or you may lose.
"Trust me, we'll work hard. It's a huge challenge to all of us and it's one we are looking forward to."