The German champions’ chairman Karl-Heinz Rummenigge revealed earlier this week that Upamecano was top of their wish list as Bayern Munich prepare for the possible departures of David Alaba and Jerome Boateng this summer.
Upamecano has emerged as one of Europe’s most sought after young defenders after the 22-year-old played an instrumental role in helping Leipzig reach the Champions League semi-finals last season.
The likes of Manchester United, Liverpool and Chelsea are all also reportedly keeping tabs on the former RB Salzburg defender.
Nagelsmann has questioned Bayern Munich’s attempts to poach Upamecano but is remaining calm about the situation.
"It's always clever to get the other team nervous, however we aren't nervous," Nagelsmann told reporters ahead of Saturday's trip to Mainz.
"We know about Upamecano's contract. We know that we want to keep him for longer and that we like to have him with us.
"You can see that, as he's playing every single game for us. But we also know the mechanisms in football. So if they want to make me or the club nervous, then it hasn't worked.
"But I don't think that this was their main intention. I believe that they said that to get a foot inside the door and make other teams that want to sign him nervous instead. But you have to ask Mr. Rummenigge, why he said what he said."
Nagelsmann added: "It is pretty normal in our business, that if a talented and young player has a buy-out clause other teams are interested in him. To what extent, someone has to then mention that publicly is up to them to assess if it's right or wrong.
"I don't have anything against it. But if it would've been the other way around, they might not have enjoyed it at all. I'm not really bothered by it. As I said already, in our business it is pretty usual. It is a part of it. Sometimes it's only about rumours but sometimes it is more concrete.
"Therefore, it isn't much of a surprise to me. Dayot Upamecano played a lot lately. I have already clarified, that some people tend to forget that he is still very young and still has to take more steps to progress further. But he is clearly capable of going those steps forward. Indeed, he had a couple of unlucky situations on the way forward."
