Why though, in response to what?
Harry Kane hasn't asked to leave. He has not. They have already denied sky's guess claims. He gave a generic interview. He talked about wanting to win things, wanting to play CL, and if he could add a player to his team (as the question was worded) , that it would be KdB. To each of those, who the fuck wouldn't! The closest he came to suggesting wanting to leave is saying he will have an honest conversation with Levy, and who knows, Levy might want to cash in and sell him.
While there is clearly an underlying suggestion in the whole thing, there is absolutely nothing of substance in it. Which is why Spurs don't need to respond. They can focus on getting a new manager in, and unless Kane Actually asks to leave, or a club make an actual offer, it is as you were and ignore the noise.
The media have managed to massively run off with this, and get everyone following, but that is all it is. For now.