The former Arsenal striker was an unused substitute as the Gunners were beaten in the final of the competition back in 2006, while he suffered an exit in the quarter-finals of the competition with United last season.
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"It would mean the world to me," the Dutchman told Uefa magazine Champions Matchday. "Of course it's a trophy many players don't win; [you win it] once, if you're very lucky. You have a couple of players who've won it more than once but it’s a very special trophy everyone wants to win every year.
"Only one team can win it, and it's very hard. It seems to get harder every year to win it, because the teams are getting better and better. So it's always hard if you want something everyone wants."
Van Persie made the move to join up with Arsene Wenger's Arsenal back in 2004, and insists that the difficult decision to leave Holland has been fully vindicated.
"Coming to England was the best thing that could have happened to me because I was taking myself out of my comfort zone, out of my nice warm city where I had my family and my friends, and everything was in place," he added.
"Suddenly 'bang', you are in a different country, you are lonely, and [you have to] deal with it. It made me tough, it made me harder and made me more focused on achieving all my goals. It made me realise that I had the biggest influence on my career, and no one else."