The Spurs star is among the contenders to lead the Three Lions in Russia this summer, with a full-time successor to Wayne Rooney yet to be appointed.
Gareth Southgate has opted to rotate the armband during his tenure, with Kane having skippered the side on four occasions.
He has netted five goals across fixtures against Scotland, Slovenia, Lithuania and France, with those exploits convincing Butcher that the 24-year-old is ready to shoulder added responsibility on the grandest of stages.
The former England captain told the Daily Mail: “I think there will always be pressure on him when you look at the number of goals he's scored for both Tottenham and for England too. So, why not make him captain?
“I think he thrives on pressure, I don't think Harry Kane worries about that. He gets on with it. He has hit the ground running with England and Spurs.
“If you provide him with chances, he is never afraid to shoot. He isn't about scoring the perfect goal, he'll happily score a scruffy goal, a mis-hit goal, do whatever you need to do to get a goal.
“He also leads the line so well, coming short, helping people go in behind, he is a good team player.
“I would like him as captain - he is young enough to be in a lot of England squads in the future so why not make him captain. Give him that pressure. He does respond well to that.”
Butcher believes Southgate’s side are capable, with it important for them to build momentum in upcoming friendly dates with the Netherlands and Italy – two fallen giants who will be absent in Russia this summer.
A man who won 77 caps for his country added: “With the way the team is shaping up in the friendlies, the way Gareth wants to play, his methods are coming across now.
“It is a good and reasonably young squad that is together, knows what they have to do and everybody knows their job. I think we are going into the World Cup very well prepared but the expectation level, for the first time, is low.
“It would be nice to win both games [against Holland and Italy] but as long as you can see some progress, cohesion, understanding and a good shape to the team, everyone will buy into it.
“It is important to have the right shape at club level but Gareth is very astute and knows what he wants. I think he will go with a back three. It is a good idea to introduce that, knowing you can easily revert to a back four.
“England are now quite pliable, which they have to be - in the past they have stuck to one and changed the personnel rather than the system.
“That will give England a lot of confidence.”