Coach Allardyce said that the Manchester United skipper was hugely respected by his peers and has enjoyed the responsibility as captain.
“You would hope the captain would make a decision on the pitch if he felt it needed to (be made).
“For me, that’s the captain’s role. It’s a big responsibility at club level and even more so at international level. First and foremost lead by example.
“It’s all about the personality. Can you handle the responsibility of being captain? I think he has enjoyed the responsibility. Some players don’t want that responsibility,” BBC quoted the 61-year-old as saying.
Rooney is England’s record goal scorer and took on the armband from Steven Gerrard last year.
The England squad is preparing for Sunday’s opening 2018 World Cup qualifier in Slovakia.