The German emerged as a leading candidate to permanently succeed Antonio Conte following his surprise sacking by Bayern Munich in March and was said to be open to the job, depending on the identity of Spurs' new director of football.
But while Spurs respect Nagelsmann, they do not consider him a good fit at this moment and the club has insisted they have not held talks with the 35-year-old and do not intend to.
Spurs first approached Nagelsmann during their chaotic 72-day search for a successor to Jose Mourinho, which resulted in Nuno Espirito Santo's ill-fated four-month spell in charge, and are understood to have sounded out his camp in the past month.
With Nagelsmann out of the running, there is even more pressure on Spurs chairman Daniel Levy to land an exciting new boss, particularly with fan-favourite Mauricio Pochettino on the verge of joining Chelsea. Spurs have not approached Pochettino about an emotional return to the club since Conte was sacked.
Former Barcelona and Spain head coach Luis Enrique is understood to be of interest, along with Sporting Lisbon’s Ruben Amorim, Feyenoord’s Arne Slot and Bayer Leverkusen's Xabi Alonso, while Brighton boss Roberto De Zerbi and Celtic’s Ange Postecoglou have also been linked.
Ryan Mason, who was put in charge after the dismissal of acting head coach Cristian Stellini, has thrown his hat into the ring for the job.
Vincent Kompany this week signed a new contract at Burnley to rule himself out of the running.
Levy is also on the hunt for a new director of football following Fabio Paratici's resignation.