Kane has told the North London side he wants to leave ahead of next season.
The 27-year-old has vowed to sit down with Levy to have a frank conversation about his future.
Levy is one of the shrewdest negotiators in world football and it had been suggested that it would take around £150m to prise Kane
However, it is understood that Levy has since increased the asking price and will only consider selling the England captain for a world record fee of over £200m.
Such a move would eclipse the £199.5m PSG paid Barcelona for Neymar in 2017.
It is unlikely that any English club would consider paying such a fee for Kane, given his history of injury problems and he will only have two years to run on his Tottenham deal in 2022.