It emerged earlier this month that Spurs ended their interest in Nagelsmann but fresh reports on Sunday claimed the German was back in contention for the job, though he wanted assurances over the identity of the club’s next sporting director.
But Tottenham insist Nagelsmann is not a contender for their vacant head coach position.
Spurs are stepping up their search for a new manager and Luis Enrique and Arne Slot have been heavily linked with the job.
Feyenoord coach Slot did not rule out a move to Tottenham on Friday but his Dutch club want him to sign a new contract. Former Spain boss Enrique is out of work.
Spurs are understood to have sounded out Nagelsmann’s camp since they sacked Antonio Conte, but earlier this month they insisted they had not held talks with and do not intend to speak to the 35-year-old.
Nagelsmann’s agent Volker Struth this week claimed the former Bayern Munich manager walked away from talks with Chelsea because the club were in “troubled waters”.
The size of the task facing the new Tottenham manager was laid bare by Saturday’s 3-1 home defeat to Brentford, which leaves Spurs in danger of missing out on European qualification for next season.
Tottenham chairman Levy is also on the hunt for a new director of football following Fabio Paratici’s resignation.