Kane has been linked with a move away from Spurs, with Manchester United among those interested.
And Jenas has likened Kane’s situation to that of Bale, who left Spurs for Real Madrid in 2013 for £85million.
Bale has gone on to win multiple Champions League and La Liga titles, while Tottenham have failed to land a trophy.
“I do feel like it is a similar situation (to Gareth Bale). I love Harry, he’s one of the best strikers in Europe but I also look at his career,” Jenas said.
“I speak to Alan Shearer a lot about the decisions he made in his career and he stands by them and has no regrets, he loves the fact that he played for his boyhood team and what he did for Newcastle and there’s a lot to be respected for that and Harry has a lot of that in him also.
“But there’s a lot of me that’s kind of looking around and going, look at what Kyle Walker has done since leaving – he’s gone and won two Premier League titles and could get to a Champions League final this year, he’s achieving things in his career and Harry is only picking up more and more injuries every year.
“I personally would encourage Harry to start having a little knock and considering another move simply from a selfish point of view as a player.
“Hopefully he doesn’t, I really hope he is more of a mindset of what Alan Shearer which was “I love this club, I love being here and I want to be here for the rest of my career”. But it’s hard for me to think without my footballer’s head on in terms of what I think would be best for him.
“I only say that because I feel like Tottenham is going in the wrong direction in comparison to where Harry Kane is going and if the ambition is not met between both club and player, I think it’s well within the player’s right to go a different way.”