Van Persie is van Gaal's captain for the Netherlands and reports have claimed that the 30-year-old will be handed the armband at United, if his fellow Dutchman takes charge at Old Trafford.
Nemanja Vidic's imminent departure for Inter Milan has created the need for a new skipper and Wayne Rooney had been tipped for the role if David Moyes had remained manager.
But, with van Gaal widely expected to be named as Moyes' replacement, Rooney's strike partner van Persie is now a candidate to be United's new captain.
"He is my captain, he's my top scorer in the one-and-a-half years that he has played under me," said van Gaal after van Persie scored in Holland's 1-1 draw with Ecuador on Saturday.
"He became the 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 missed large parts of United's disappointing season through injury as the club failed to qualify for Europe after finishing seventh in the Premier League.
It was a stark contrast to van Persie's first season at United when his goals helped to win the title, but he is optimistic the future will be brighter.
The former Arsenal forward, who recently returned after nearly two months out with a knee injury, said: "I followed everything from a distance, as the club had allowed me to do my rehab in Holland.
"It was good to have some distance, 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. That's [van Gaal's appointment] something for later on."