Germany and Bayern legend Lothar Matthaus, now a TV analyst, claimed Nagelsmann is the top candidate to replace Hansi Flick, should he leave in order to take over the Germany national team role in the summer, and contact had already been made.
"There have been no talks and we are currently in no talks," Nagelsmann told a news conference on Wednesday ahead of Leipzig's Bundesliga match against Hoffenheim.
"The country needs new sources. I don't know where he got his info from.
"It's not like they [Nagelmann's agents] are acting autocratically. They do things I ask them to. And thus, there were no talks."
Having joined Leipzig from Hoffenheim in 2019, Nagelsmann reached the Champions League semifinal last season and they are second in the Bundesliga this season.
Despite saying there had been no talks, the 33-year-old did not entirely rule out joining Bayern at the end of the season.
"There are always developments in football you can't foresee," he added.
Following Bayern's exit from the Champions League on Tuesday, Bayern coach Flick admitted for the first time he is thinking about his future which could see him take over the Germany job once Joachim Low leaves his post after the European Championship.
"I must talk those things through with my family," Flick said. "The family has always supported me in the past and will do so in the future. It's a good feeling. And it would not matter to them if I were at the DFB [the German Football Association] and had a different rhythm."
Flick worked as Low's assistant from 2006 to 2014. He took over as Bayern's head coach after the sacking of Niko Kovac in November 2019.
He went on to win the sextuple in his first season and is on course for a title defence in Bundesliga.
A row between him and sporting executive Hasan Salihamidzic over the club's transfer philosophy has added fuel to rumours of his possible return to the national team.