Current Netherlands coach Van Gaal is widely expected to take the reins at United following this year's FIFA World Cup, with his appointment reportedly set to be announced before the tournament.
The club's captaincy is up for grabs as former incumbent Nemanja Vidic is joining Inter ahead of the 2014-15 campaign.
Van Persie is Van Gaal's skipper at international level, and the former Barcelona and Bayern Munich boss lauded the striker's ability and leadership qualities after seeing him score a wonderful goal in his side's 1-1 friendly draw with Ecuador on Saturday - labelling him a "fantastic captain".
"He (Van Persie) is my captain, he's my top scorer in the one-and-a-half years that he has played for me," the 62-year-old is quoted as saying.
"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."
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