The Dutch forward is joint-top scorer in the Premier League with 12 goals after 17 games as the Red Devils sit top of the table by three points, while he has also netted three times in four European matches.
And the striker's 61-year-old international coach thinks the former Gunners favourite can keep improving and extend his international career if he keeps up his fine club form.
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"Robin van Persie is getting better and better - it's incredible," Van Gaal told reporters. "He is a super professional player who really knows what he wants from his career and how he will achieve it.
"I have never seen any player reach Robin's age and still improve as a footballer. Van Persie is more aware than any other player I have worked with of the possibilities open to him.
"He is convinced he can get better every week - even at his age - and that's probably why he continues to improve while others don't."
Van Gaal suggests it would have been easy for Van Persie to assert his dominance at Old Trafford and settle down, but the manager is impressed by the forward's willingness to keep improving his game.
"His personal development is amazing," the former Barcelona boss enthused.
"Robin could be another leader at United if he really wanted to. But when he signed for the club he told me he was determined not to act as the big man with the other players.
"He wanted to concentrate on his own game, to make the best of himself at his new club. That attitude really sums up his character."
And the coach is also delighted with Van Persie's form in that he has given Van Gaal more selection problems for the future.
He added: "Moving to United has been good for him - and it has been good for Holland.
"I had never worked with him before and the first thing he told me was that if I kept him on the bench he would work even harder to prove me wrong.
"He said he would never walk away from Holland - and I absolutely loved that about him."