Gareth Southgate is looking to name a new skipper now that Wayne Rooney's international career is seemingly winding down, and Kane staked his claim by rescuing a point for the Three Lions with a stoppage-time equaliser at Hampden Park on Saturday.
The Tottenham striker, who has topped the Premier League scoring charts for the past two seasons, is hopeful he will be selected as the new main man for England.
"I would love to be England captain," Kane told reporters. "Obviously I do not know what the gaffer's feeling is on it.
"A good captain leads by example. On and off the pitch. You have a responsibility off the pitch with the media, kids coming through and being a role model.
"I am quite a calm character. I am not someone who gets too irate or too low. I have a steady mind and I know my ambitions. I know what I want to do and this team has great ambition. I am one of many who could be captain.
"It was quite emotional when Southgate told me I would be captain against Scotland. He told me just before training on Friday.
"[There were] a lot of emotions, lots of proud feelings and when I got back I told my family and my missus. They were delighted. It was something I have always dreamed about as most kids do.
"So, to be given that opportunity by the gaffer and how the game panned out, to manage to score in the last minute was a very proud moment."