The 23-year-old remains an influential figure for England, despite failing to live up to expectations during the country's woeful Euro 2016 campaign.
"It's my personality. I've always been a leader, on and off the pitch. I don't think a captain is just having the ability to shout on the pitch, or moan at someone," Kane said in an interview with the Times.
"It comes with a whole package ... meeting with the fans and having that aura in the dressing room. I've managed to captain Spurs a couple of times. It would be a dream to captain Spurs full time and captain England. Who wouldn't want to do that?"
Kane also lauded Pochettino's bravery for giving youth a chance rather than taking the easy route of buying experienced players.
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"Spurs give young players a chance. A lot of that is down to the manager. It takes a brave manager to go and do it," Kane added.
"It is easy nowadays with the money. There's a lot of players you can buy, so you can just get experienced players you know can do a job, who might not be as good as the young players coming through but it's less of a risk."
Fifth-placed Tottenham host London rivals West Ham United, who are 17th in the league, on Saturday night.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Nick Mulvenney)
