Kane will go a 13th successive season at Spurs without a trophy after the club’s deflating Champions League exit.
Antonio Conte’s side were beaten 1-0 by AC Milan over two legs to crash out of the Champions League at the last-16 stage.
Tottenham’s exit looks set to spark fresh speculation over Kane’s future, with the 29-year-old linked with the likes of Manchester United and Manchester City in recent years.
Arsenal legend Henry believes Kane should be looking for a new club and says the ‘outstanding’ England striker is too good to finish his career without any trophies.
‘If I was him I would go,’ Henry told CBS Sports. ‘It’s up for him to choose where but I would go, he has to know where he wants to go.
‘A player like that, a player of his calibre, should not talk about just his goals at the end of his career. If I was him, I wouldn’t be able to sleep at night if all I could talk about is my goals.
‘Listen, it’s a great achievement and I have massive respect for him – I think he’s outstanding. But if that’s the only thing you can bring to the table at the end of your career, that’s tough for me.’
Kane has scored a record 268 goals in 423 appearances for Tottenham and is chasing Alan Shearer’s all-time Premier League tally.
As a result, former Liverpool defender Carragher believes Kane will be keen to stay in England if he does leave Tottenham but admits there are not a great deal of options for the striker.
‘The big question now is about Harry Kane,’ he said after Spurs’ European exit. ‘If he doesn’t leave this summer, he will stay at Tottenham for the rest of his career. I think it’s now or never for him.
‘Tottenham will always be there or thereabouts in terms of qualifying for the Champions League but will he win trophies? No. He’s never won a trophy in his life.
‘If you’re asking me if he should leave to join a team to win a domestic cup or stay at Tottenham I think I would stay. But this is a guy who should be going deep in the Champions League every year, he’s that good.
‘Where does he go? That’s the big question. There’s not too many clubs there right now for him. In terms of what’s happened at Tottenham, I think it’s pretty negative.
‘I think the only place he can go realistically is Manchester United. I don’t want to see him there for obvious reasons but Man City have Haaland, Liverpool have Nunez, he can’t go to Arsenal or Chelsea.
‘He could go abroad but he will want that Premier League goal. He will be the top goalscorer if he stays in the Premier League and that is a pretty special achievement.
‘So if he stays in England, the only big team he can go to is Man United. But will they spend £100m for a guy who is nearly 30?’
MORE : Antonio Conte claims Tottenham have made step forward despite AC Milan defeat
MORE : Liverpool legend Jamie Carragher ‘delighted’ PSG are out of Champions League
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