Kane captained England against France and Scotland earlier this year but Liverpool’s Jordan Henderson was made skipper for the Three Lions’ recent victories over Slovakia and Malta.
England boss Gareth Southgate is yet to appoint a permanent successor to Wayne Rooney, who announced his international retirement earlier this season, but he is going to make a decision before next summer’s World Cup in Russia.
Kane, who scored 13 goals for club and country during September, feels ready for the responsibility of leading the national team.
“Yes, I’ve had the armband and it was a very proud moment,” said the Spurs vice-captain.
“I feel like one of the leaders in the team. But Gareth Southgate has said he is going to take his time and we do have plenty of leaders.
“Whoever Gareth picks as captain, the team will get behind him. We have still not qualified and we have to win the game on Thursday, and that makes it easier on Sunday.”