The England striker is making motions towards the Tottenham exit door after growing tired of their lack of success.
But, with three years still left on the 27-year-old’s contract, any prospective buyer will have to convince Spurs chairman Levy.
According to the Mail, an absolute minimum fee of £150million will have to be produced.
Manchester City offered £100m last month with Chelsea and Manchester United also monitoring the situation.
Pep Guardiola’s side told Spurs they were open to including Raheem Sterling, Gabriel Jesus or Aymeric Laporte in a potential deal.
But Levy has held firm in his belief that Kane is going nowhere, having finally signed up a new manager.
Nuno’s arrival was confirmed on Thursday after the likes of Antonio Conte, Paulo Fonseca and Mauricio Pochettino came and went from the Spurs shortlist.
Among his first tasks will be trying to convince Kane to stay.
The striker is currently focused on England’s Euro 2020 run and will not address his future until the tournament’s end.