Nagelsmann will leave TSG for RB Leipzig at the end of this season - but admits he has ambitions beyond the East Germans.
While Bayern Munich is a goal, the 31 year-old is also attracted by the Reds.
"It's a nice club. Of course, one day I can imagine being a coach there, but I can also do it with Liverpool or Barça," he told BILD.
"In a maximum of six years I want to win something."