Leipzig boss Nagelsmann is considered one of the most promising coaches in European football and led his team to the UEFA Champions League semi-finals last season.
The 33-year-old, who has a contract at Leipzig until 2023, has been touted as a candidate to take over Dortmund next season, with Edin Terzic having replaced Favre on an interim basis in December.
However, Nagelsmann insists there is no need for anyone associated with Leipzig to worry about what the future holds because he intends to stay put.
"There is no reason to be tense regarding Dortmund," Nagelsmann said ahead of a Bundesliga meeting with Dortmund on Sunday (AEDT).
"The situation with Dortmund has remained the same as it was during my time as Hoffenheim coach. There was and there is no match.
"I am comfortable and I have big targets to achieve with Leipzig. As I said, there is no reason for anyone at RB Leipzig to get nervous regarding Dortmund."
Leipzig sits second on the Bundesliga table, six points ahead of fourth-placed Dortmund and two adrift of leader Bayern Munich.
Asked about Nagelsmann during a pre-match news conference on Thursday, Dortmund sporting director Michael Zorc said: "Despite his age, Julian has had a remarkable managerial career. With Hoffenheim, he was able to work sensationally well, now he's having a just as sensational season with Leipzig.
"I believe, it is undisputed that he's a complete football expert. He always implements innovation into his coaching technique. He is always able to get his team to work well.
"We need to try to fight against that on Saturday [Sunday AEDT]. We already came up against each other a few times and it's not like we had no success at all in these match-ups.
"I see ourselves, also due to the position in the table, in the role of the hunter. We want to minimise the gap between us and to the top of the table."