Rooney shared the responsibility with Darren Fletcher and Tom Cleverley on the club's recent pre-season tour of the USA, while some reports had suggested that Van Gaal would opt for Robin van Persie, who captained the Netherlands under his management.
However, BT Sport pundit Savage believes that a lack of leaders at Old Trafford meant that Van Gaal's selection of Rooney was the "right decision".
"If you look at the experience in that side, they've lost Evra, Ferdinand, Vidic and Giggs, so the natural leader is Rooney. He is a great player, unselfish and it's going to be a really big season for him. He should be England captain as well," Savage told Sports Mole.
"The other candidate was Van Persie, who is a great leader for Holland, but the right decision has been made because Rooney was the real standout option.
"In teams gone by, there has been a host of leaders. Gary Pallister, Steve Bruce, Roy Keane, Paul Scholes, Gary Neville and so on. There was leaders all over the pitch. You could have given the armband to five or six players, but that is not the case now."
Rooney joined United in the summer of 2004 from Everton.
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