Van Gaal's arrival at Old Trafford has seen the emergence of Smalling, who has developed into one of the Premier League's most consistent defenders since the Dutchman replaced David Moyes last year.
Rooney is the current captain but Van Gaal believes the quick-learning 25-year-old Smalling has the potential to skipper United in the future once the current holder steps down.
He said: "Wayne Rooney is the captain, so you don't have worry, and then Michael Carrick [vice-captain].
"But when they are gone then, Chris Smalling can do that. So I push him in that situation.
"Every player makes the steps by himself. I put him in the situation, I help him in the situation and I advise, and the player can take it on board or not.
"It's his responsibility. He's done it by himself. There's a lot of advice and it's about how we defend as a team.
"He's a part of that and I wanted him to speak. He also has the talent to speak. That makes him easy to coach.
"Because of that, I have made him a leader of the team. He's made steps, and also in a tactical way.
"When you give instructions in terms of organisation, you need someone to understand that. He's a structured person and he accepted it more quicker.
"David De Gea has the best view [of the game] and then the central defenders, so I demand of my defenders that they speak.
"They also need an overview. I put him [Smalling] in that situation and then he can develop or not. It’s his choice."