The two parties were due to meet on Friday but the face-to-face meeting has now been postponed.
Bayern had a £70million offer for the England captain rejected earlier this month but are readying an improved bid.
Kane's advisers have indicated he is open to joining the Bundesliga champions.
The striker, who turns 30 today, has entered the final year of his Tottenham contract and talkSPORT understands he is not interested in a new deal despite being offered £400,000-a-week.
Levy values Kane at £100m and it is thought Bayern are willing to pay up to £86m.
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The German giants can wait to strike a pre-contract agreement with Kane in January ahead of a free transfer - although they may face increased competition.
Paris Saint-Germain are also interested in signing Kane, while Manchester United could re-enter the mix if he becomes available for free.
Levy is known to be a fierce negotiator, having denied Kane a £125m move to Manchester City in 2021.
The Tottenham striker has since overtaken Jimmy Greaves as the club's all-time leading goalscorer with 280 in all competitions.
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Newcastle legend Alan Shearer has the most Premier League goals in history with 260 and Kane is second on 213.
Many expected Kane would push to stay in England but Levy appears less reluctant to talk with foreign clubs.
Kane has spent 19 years at Tottenham, arriving as an 11-year-old in 2004, but has no major trophies to show for his incredible service to the club.