The 30-year-old is regarded as the hottest property in the Bundesliga after guiding his side away from relegation in 2015-16, and then securing a fourth-place finish – earning a European berth.
After 15 games of the current campaign Hoffenheim sit sixth in the table, but how long Nagelsmann – who signed a deal until 2021 in June – will remain at Rhein-Neckar-Arena remains the subject of much debate.
With Bayern sacking Carlo Ancelotti in September and Dortmund dismissing Peter Bosz on Sunday, both have installed interim managers – Jupp Heynckes and Peter Stoger respectively – until the end of the season.
Nagelsmann has been touted as replacement at both of Germany's big two, but Hitzfeld – who has managed both clubs – says he should stay loyal to Hoffenheim for now.
Speaking to Sky, the 68-year-old said: "If someone like that [Nagelsmann] is with Dortmund at the age of 31, then I ask myself: What is he still doing after that? What goals does he still have at 40?"
"Nagelsmann is a good coach, but I think it's generally important to keep contracts, because you have a lot to thank the club for."