The striker has been Netherlands skipper for the past year and a half and demonstrated his authority with a brilliant volley in his country's 1-1 draw with Ecuador earlier this week.
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“He is my captain,” he said. “He is my top scorer in the one-and-a-half years that he has played under me. He became all-time top scorer of the Dutch team, he plays superb football and even coming back from a bad injury, he scores a fantastic, unbelievable goal.
“I was happy with his performance, but he is also a fantastic captain. I think you always make a player captain when you have the same morals and philosophy.
“Not only about football and tactics and what is happening on the pitch but about life. I think that’s very important and I believe that Van Persie and Van Gaal share the same philosophy.”
Van Persie refused to be drawn on the identity of David Moyes' successor at Old Trafford but did suggest that the future at the club is bright, despite this season's seventh-placed finish.
“I followed everything from a distance, as the club had allowed me to do my rehab in Holland,” he said. “It was good to have some distance because it has been a tough year.
“For the first time in my career, I won’t be playing in Europe.
“It was a huge difference between this season and the last one, but it’s our job to switch a button now. Everything is going to be all right with the club.”
Van Gaal could be announced as United boss over the coming days.