The man who won the FA Cup with Spurs in 1991 was quizzed by Laura Woods on the Breakfast Show about Kane’s future.
Kane has quickly become one of the world’s best centre forwards with 181 goals in 278 appearances for Tottenham.
That sort of ratio is bound to attract suitors at home and abroad and Lineker believes he will have a decision to make.
He told Talk Sport: “He could possibly go abroad. There are a lot of players who feel uncomfortable about doing that though.
“At home, you look at Manchester City, Sergio Aguero is 32 and Manchester United, well they definitely need to sign a centre-forward. He’s got one or two options.
“Barcelona could replace Luis Suarez, Real Madrid, to replace Benzema.”
Tottenham would almost certainly command a world record fee if they were to consider selling Kane.
The world-class striker would be almost irreplaceable at the Tottenham Hotspur Stadium.
It has been previously mentioned by The Telegraph that Daniel Levy would try and get £250 million for his star man.
With that in mind, any club will need to dig deep to secure the England captain.
Jose Mourinho will desperately want to avoid failure with Spurs and will want Kane to spearhead his attack.
Winning trophies could be key, however, and although the 26-year-old is a self-confessed Spurs fan, silverware will be important.
With that in mind, Tottenham might need to start preparing contingency plans.
It’d certainly be interesting to see whether he would prefer a move to another Premier League club or one overseas.