"Wat Van Gaal will have seen while watching him train every day is that he has passed the armband to the most intense player at that football club, with a ferocious attitude and tough mentality," Neville wrote in his Daily Telegraph column.
"There has been a sharp decline in leadership in football but Rooney has all the attributes.
"By 'leaders' I mean people who are prepared not only to hold themselves accountable but hold their team-mates accountable too.
"Rooney is one of a dying breed of footballers who is willing to call his team-mates out. He can take criticism but also hand it out. His approach is the traditional one of not taking criticism personally - and expecting team-mates not to take it personally either.
"Van Gaal will have looked at Rooney and thought: this is a player who is not too proud to listen to criticism and not too shy to dish it out. That is captaincy material, as Van Gaal outlined in his press conference ahead of the Swansea match. The next stage for Rooney is to think like a captain.
"When I think back to his early days at United I remember his personality and cheekiness. Rooney was the only player who would dare pull up a seat at the coaches' table in the canteen and ask Sir Alex Ferguson: "Am I playing tomorrow, boss?" The manager would cuff him about the head and say: "That's nothing to do with you...
"He is one of the few footballers I watch now who could have survived 20 years ago, in what was a more brutal environment, where every decision in training was challenged, where he would have wired into his goalkeeper if he made a mistake, where being vocal was a virtue rather than the mark of a troublemaker.
"Ten minutes after calling a team-mate out, he would join them on a sofa, returning to friendship mode. He pays no attention to age, seniority or reputation."
Rooney, meanwhile, has described being handed the United captaincy as an honour.
"It's a massive role to take on - I'm aware of that, the responsibility of it - and I feel I'm ready at this stage in my career to do it," the 28-year-old forward told United Uncovered.
"I spoke to the manager and he decided that I was right to take the role which I am delighted with. It's a great honour.
"I will perform the role as best I can and hopefully help the team to be successful."
Rooney is set to captain United when they kick off their Premier League campaign against Swansea at Old Trafford on Saturday.
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