Van Persie has signed a four-year deal with the Old Trafford club, who paid the Gunners €30.5 million for his services, and Muhren has said that the Dutchman’s move to Manchester was to be expected.
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"It would have been City or United," he told Dutch newspaper Algemeen Dagblad.
"I understand his choice. Manchester United is one of the biggest clubs in the world.
"If he wants to win prizes, he has the chance at United, they have a very good team with that new kid from Dortmund [Shinji Kagawa], Rooney, Hernandez, Valencia and Nani, and the young lads that are breaking through."
However, Muhren did have some words of caution for his countryman, as he looks to adapt to a different role from the one that he had at Arsenal, particularly last season when he scored 30 goals in the Premier League.
He added: "At Arsenal, everything turned around him. At United that's going to be different. There are some egos at United, so he will have to find his way here.
"He's a guarantee for goals, and he makes 20 or 25 a season. If he makes 15, the other players will score more.
"He came to Old Trafford to win prizes, and I have a lot of faith in that."