Nagelsmann has many admirers following a successful stint at Hoffenheim, and now with Leipzig.
He has led his current side to within a point of Bayern Munich at the top of the Bundesliga and represent a difficult proposition in the Champions League, particularly following news of the injury to Spurs forward Son Hueng-min.
And Mourinho was asked whether he had been following Nagelsmann’s rise and whether he represents a new generation of coaches.
Ahead of the Champions League last-16 tie, Mourinho said: “What’s that? New coach generation?
“The opponent is Liepzig. I don’t have an opponent’s coach. I don’t play against him. I play against his team Leipzig.
“Hoffenheim before. Did very well. Next step Leipzig. Doing very well. If he goes in the same direction the next step will be even bigger. I wish him obviously the best.
The 32-year-old was linked with the Tottenham job before Mauricio Pochettino was sacked, and Mourinho was asked whether that meant he had something to prove.
He added: “To prove? After 20 years of career and 25 titles, to prove?”