The 29-year-old Dutchman joined the Premier League outfit at the beginning of the previous campaign after opting to end his eight-year stint with Arsenal.
He impressed immediately, slipping directly into a first-team spot and going on to score 26 goals in 38 league appearances to retain his golden boot award.
However, despite helping to guide United to the league title comfortably ahead of rivals Manchester City, he still wants more.
"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," he said.
"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."
United will go into next season without esteemed manager Alex Ferguson, who retired from the role after 25 years in May, and have already begun life under his replacement David Moyes.
Their pre-season preparations have already commenced well, with the second game of their tour of Asia ending 5-1 against the A-League All Stars but Van Persie knows City will be a strong contest for them in the upcoming campaign.
"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," he added.
"Trust me, we'll work hard. It's a huge challenge to all of us and it's one we are looking forward to."
Moyes' side will continue their tour with a match against Yokohama F-Marinos on Tuesday before facing Cerezo Osako three days later.
