The manager, who will take charge at Old Trafford after the World Cup, was coy when questioned on his interest in the Roma star and reiterated his excitement at his new role
The 62-year-old was confirmed as the club's new manager on Monday, with his three-year deal set to start following his commitments with the Netherlands at the World Cup.
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"Success at United doesn't depend on money, but about which players we bring in," he told NOS. "I gave my wishlist to the club. Is Kevin Strootman on it? A question for you, a fact for me."
Van Gaal is confident heading into his new role, revealing his excitement at taking charge of "the biggest club in the world," but again insisted his current focus is on Netherlands' World Cup campaign.
He continued: "It's not hard at all to make the switch from United to Oranje. For a manager it's totally different then for a player.
"A player needs to focus on one thing to be successful, while a coach is thinking about the whole process. Otherwise I couldn't do interviews like this any more and that's just ridiculous.
"In October I said that I wanted to work in the Premier League. But I couldn't expect that I would work for the biggest club in the world.
"Barcelona is maybe the best club in the world and Bayern Munich is the best organised club in the world. But Manchester made a very professional impression on me. I've got high expectations.
"Of course I have ambition to become World Champions with Oranje. I'm not going to Brazil just to take part of the World Cup, I'm trying to win it. That's why we're looking for a system that makes us unbeatable."