The 23-year-old is currently sidelined with an ankle problem and has therefore not been included in Gareth Southgate's squad for upcoming games against Germany and Lithuania.
But widespread reports suggest Kane is being considered as a potential long-term replacement for Wayne Rooney, who is no longer a guaranteed starter for the Three Lions, after Southgate hailed Kane's leadership qualities last week.
Kane, who has already worn the Spurs armband with distinction on several occasions, has previously spoken of his desire to succeed Hugo Lloris as skipper.
And while Pochettino was reluctant to discuss a decision that rests with Southgate extensively, the Argentine coach believes Kane ticks the boxes needed for a leader at both club and international level.
"This is his opinion - it's not my decision," Pochettino said of claims Southgate could name Kane his permanent England captain.
"I explain how I see Harry Kane. For me he's a leader and why can't he be captain one day of the national team and Tottenham too?"
Kane worked under Southgate within England's Under-21 set up and the striker is rated highly by the new Three Lions boss.
“Harry has definite leadership qualities,” said Southgate. “Harry’s got an opinion. He’s always happy to speak up in front of the group.”