Kane scored twice in his side's 2-1 win over Rangers on Saturday, with the England striker looking sharp heading into the new Premier League - or Bundesliga - season.
Nagelsmann stated that Kane was a 'brilliant player' and claimed that he'll 'see what happens' regarding a move for the centre-forward, after Bayern sold Robert Lewandowski to Barcelona.
But Conte wasn't best pleased with the German's comments and stated that it was 'disrespectful' to talk about other clubs' players.
"Honestly I didn't hear this. For sure I'm a coach who doesn't talk about players from other teams. I don't know why [this happened]," the Italian explained.
"The situation at Tottenham is very clear. The plan is very clear with the club. Harry is a part of the project. He is a very important part of the project and, yeah, only rumours.
"At the same time, I repeat I don't like to speak about players from another club. If I want to do something I go to speak to the club, not through the media.
"I think maybe it's a bit disrespectful for the other club. This is my way. This is my way to face the situation with other players."
And Kane's teammate Eric Dier insists that it's 'normal' that world-class players will receive praise from other managers.
"Yeah, that's normal now. I think every world-class player is always going to be spoken about a lot," the Spurs defender said.
"In football, you don't know what's going to happen tomorrow, let alone next week.
"It's not something I'm really bothered about, it's just normal that you know world-class players are spoken about a lot."