Kane faces a battle to force his way out of the club after the tournament, while Spurs' search for a new manager took yet another dramatic twist on Thursday when they called off a move for Paulo Fonseca and opened talks with Gennaro Gattuso.
The striker will lead England out against Scotland at Wembley in their second group game of the tournament, and they can reach the knockouts with a game to spare by following the 1-0 win over Croatia with another three points.
Asked if the Spurs circus and speculation about his own future were proving distractions, Kane said: “It's very rare to have a home tournament and for me personally, this is as close as it's going to get. We've got to try to use that to our advantage as much as possible.
"That's all I'm focused on. It's obviously a massive tournament and I know how much it means to the country. We know we haven't won a major trophy for a long, long time so to try to achieve that with a lot of the games at Wembley, our home stadium, would be incredible.
“That's all I'm focused on, that's all the team are focused on and we'll do our very best to, as first step, qualify tomorrow night and then hopefully go as far as possible after that.
“Tomorrow night is going to be a tough game," he added. "There has been a lot of build-up around it. But it is our second game at a major tournament and our focus is to try to win and make sure we try to qualify tomorrow night and give ourselves as much of a chance of getting through as early as possible.
“That's all we are focused on. We know there is a lot of build-up around it but we're just trying to stay focused on us and what we need to do."
Kane insisted England genuinely believe they go can all the way and win the tournament, adding that failing to at least match their run to the World Cup semi-final three years ago would be a disappointment.
"We all have to believe we can win it," he said. "That’s the reason we’re in this competition to try to win it. Every player has belief in themselves first and foremost and belief in each other and I think that’s what makes a really strong team.
“That’s the only way you’re going to get far in tournaments.
"Of course we believe we can win it. We also understand it hasn’t been done for our country for a long time and there’s a lot of hard work along the hopefully seven games that we play.
“From my point of view of course it’s been a dream since I was a kid to win a tournament and lift a trophy with England and to have that opportunity now is exciting. Hopefully I can use all those good feelings to our advantage.
"If we fell short of a semi-final, we’d all be disappointed as players, as a country and as staff as well.
"I think we have been moving in the right direction in the last three or four years so the next step is to go one step further, at least, and try and get into that final and hopefully try and win it."