Chelsea have struggled to find a player to lead the line this season, with Diego Costa failing to find his best form.
And Le Tissier believes that Jose Mourinho would love Kane to join him at Stamford Bridge, but he doubts Tottenham would be willing to listen to offers.
"I think Chelsea would love him [Kane] in January. Whether or not they’ll get him, I doubt it," Le Tissier said.
"With Spurs down the years it has been the case [that they have sold players]. But it might be different with Kane, and he might be different – and decide that he wants to stay for a while. That would be great news for the Tottenham fans."
Kane has been in wonderful form for Spurs so far this season, and he has coped the responsibility handed to him by Mauricio Pochettino admirably.
Although the front-man is still only 22-years-old, he has coped with the demands of being Tottenham’s only number nine and has gone from strength to strength.
The England international has netted nine times in his last seven matches, and his excellent goalscoring form has helped Spurs establish themselves as top-four contenders.
Tottenham have gone unbeaten in their last 13 Premier League matches, and they are only two-points away from the Champions League qualification spaces.
To lose Kane after such a good start would be virtually unthinkable, and it does seem very unlikely that Chelsea would be able to force through a deal for the front-man, even if they did launch a bid.