Executives from the Munich giants had reportedly been due to meet with Levy on Friday to discuss Kane, with the England captain being heavily linked with a switch to Allianz Arena.
However, according to talkSPORT, the face-to-face meeting has been pushed back to Monday.
The speculation surrounding Kane's future is gathering pace, as it is understood that Tottenham owner Joe Lewis will sell the 30-year-old this summer if he refuses to sign a new deal.
Lewis is allegedly not prepared to run the risk of losing the Three Lions skipper on a free transfer next year and is therefore planning a big-money sale this summer unless the forward commits to the club.
Manchester United are still said to be keeping a close eye on the situation, while a recent report claimed that Paris Saint-Germain are in the race for the centre-forward.
Bayern remain the favourites, though, with their president Herbert Hainer recently confirming the club's interest in Kane, who is valued by Spurs in the region of £100m.
The Bundesliga champions are thought to have already failed with two offers for the forward but are now believed to be preparing a bid in excess of £86m, which could be accepted.
Tottenham have allegedly offered Kane the chance to sign a new contract worth £400,000 a week, but he is not thought to be willing to pen a deal while the transfer window remains open.
The forward was again in excellent form for Spurs during the 2022-23 campaign, scoring 32 times in all competitions, including 30 goals in the Premier League.
However, the North London club finished down in eighth position in the table, meaning that there will not be any European football at the Tottenham Hotspur Stadium in the coming season.
Bayern head coach Thomas Tuchel is believed to have recently met with Kane at his London home, and the forward is thought to be confident of winning the Champions League at Bayern.
The striker, amid the speculation surrounding his future, is involved in Tottenham's pre-season, and he scored in their 5-1 win over Lion City Sailors on Wednesday.
Bayern are in the market for a new centre-forward this summer, having allowed goal machine Robert Lewandowski to make the move to Barcelona last year.