Kane is currently on Tottenham's pre-season tour of Asia
Bayern Munich have had two bids rejected for Kane, 29, and met with Tottenham chairman Daniel Levy.
Manchester United also enquired but backed off when informed how much a deal would cost them.
The England captain's contract at Spurs expires next summer.
Tottenham have given the impression they are prepared to let Kane enter the final year of his contract.
However, that is a risky strategy as Kane could sign a pre-contract agreement with an overseas club in January or join a Premier League rival for nothing next summer.
In the 2019-20 season, Tottenham faced a similar position with Christian Eriksen. They held onto the Danish midfielder until the January, when they eventually sold him to Inter Milan.
There is a feeling within the game that Tottenham do not want to lose Kane without generating some revenue and that they could eventually buckle, which is why there is a log-jam around a number of Europe's leading strikers.
Juventus' Serbian striker Dusan Vlahovic, 23, and Eintracht Frankfurt's French forward Randal Kolo Muani, 24, have plenty of admirers.
Bayern would be a serious option for both players but the Bundesliga giants will not move for either until they have satisfied themselves they cannot get Kane.
Paris St-Germain look increasingly like needing a new striker given the Kylian Mbappe situation, with the club looking to sell the France forward, who is entering the last year of his contract.
-- Courtesy of BBC Sport