The England international is enjoying a prolific 2020/21 campaign, making 40 appearances for Tottenham in all competitions, while netting 27 goals and providing 16 assists.
After reaching the Champions League final in 2019, Spurs were knocked out in the round of 16 stage of the competition last season by German outfit RB Leipzig.
Kane missed out on Champions League football this season as Tottenham were unable to make the top four last time around.
Speculation is growing that Kane may look to leave Tottenham as he aims to win the biggest trophies in the game, but former Premier League star Burley thinks he may have missed his chance.
Burley feels that top sides will look at Kane and feel that given his age they will not get the value out of him needed to justify a big fee.
“I just wonder if the ship is sailing for Harry Kane”, Burley said on ESPN FC.
“He needs to get a move on, I think, in terms of a move.”
And Burley added: “I wonder whether a club will shell out huge money now for Kane, depending on the fee.
“I think two or three years ago, at 26, 25, that’s absolutely prime, he’s got another five, six, seven years, that’s good value for a club.
“But two or three years, four at a stretch and he’s had injuries, no.”
Tottenham are still battling to try to finish in the top four this season and if they can secure Champions League football it could banish questions over Kane’s future.