Speaking to Melissa Reddy of The Indepedent, Nagelsmann admitted Real Madrid approached him about becoming manager ahead of the 2018-19 season. Zinedine Zidane had walked away from the club in 2018, having steered Los Blancos to a trio of consecutive UEFA Champions League titles.
The German boss said he spoke to key figures at the La Liga giants but decided the move wasn't right for him at that stage of his career:
"It's normal if Real Madrid call you, you think about it. I was surprised at first, I weighed it up and I didn't feel comfortable with a decision to go there. I want to improve. If you go to Real Madrid, there's no time to improve as a manager.
"You don't have a chance to be a better manager, you already have to be the best. I'm not the best now, but I can admit I want to be one of the best in future. If you go to Real Madrid or Barcelona, the fans, the media and the decision-makers don't give you the time to grow into that."
Nagelsmann added that he was concerned about the language barrier, with his knowledge of Spanish not extensive.
The 32-year-old is regarded as one of the brightest managers in world football, having excelled with Hoffenheim before his switch to Leipzig. With Hoffenheim, he pulled the team out of relegation trouble in the 2015-16 season, then steered them to fourth and third in the following campaigns.
He's transformed Leipzig into Bundesliga challengers, and they sit a point behind Bayern Munich ahead of the Week 22 fixtures.
He's been an ever present in German football since being appointed:
The coach has issued some harsh words to his Leipzig players at times this season, despite their generally high performance levels:
Nagelsmann has also been linked with a switch to English football in the past, and he said the Premier League is something that would interest him further down the line:
"The Premier League interests me as do other clubs in the Bundesliga and La Liga, but I have to improve my Spanish first. I know it's very tough in England. I've been reading the interviews of [Jurgen] Klopp and Guardiola about the intense fixture schedule and the demands on players and staff."
For Nagelsmann, getting Leipzig to the summit of German football will be a big challenge, especially with the might of Bayern Munich to compete with.
However, throughout his career he has outperformed expectations due to smart management and overseeing savvy recruitment. With that in mind, it's no shock he's already desired by so many huge names.