The Dutchman moved to Old Trafford from Arsenal having won only two medals in his career. The 2002 UEFA Cup with Feyenoord and the 2005 FA Cup with Arsenal.
Van Persie, 29, is set to win his first league title in his first season with United. United are 15 points ahead of rivals Manchester City with only eight games left in the season. The Red Devils are still in the FA Cup with a quater-final replay against Chelsea on Monday.
"That I'll probably win my first championship is very nice," Van Persie said. "I'm really thrilled about it. Not winning titles has given me quite some pain.
United visit the Stadium of Light on Saturday and then face Chelsea in the FA Cup. Despite being 15 points clear with City yet to visit Old Trafford, Van Persie said it is still not over.
"It still has to happen," he said. "We have to go to Sunderland and West Ham, and we have to play Chelsea. If we win, we play back-to-back against City in the league and the FA Cup semi-final.
"Then we have Stoke. These are not summer night games. I watched United drop the lead last season, but it's getting awfully close now and I'm really happy with that," he added.
Van Persie has 19 league goals this season but has scored only one in 10 games. The Dutch striker last scored in February but netted three goals in two games in World Cup qualifiers against Estonia and Romania.
"The key is to keep working hard. I've also missed some luck. If you analyse my chances, my efforts went just over or on or next to the woodwork," he said.