Kane raised the possibility of leaving Spurs back in March, when he admitted he would have to move on if he could not fulfil his ambition of winning trophies in north London.
The England captain has been linked with a summer move to Manchester United, though Standard Sport understands Spurs have no intention of selling, particularly not to a Premier League rival.
Sheringham made the move to Old Trafford in 1997, but insists the gulf between the sides at that time made the switch something of a no-brainer.
“There are similarities,” he told Sky Sports. “But you have to look at Tottenham where they are and where they were when I was playing for Tottenham.
“The ambition had been sucked out the club when I was playing for Tottenham, we weren’t really going places. At least with Tottenham at the moment they’re getting into the top four. They’re challenging for things. In the Champions League final not so long ago.
“He’s got to weigh up his situation, does he want to leave? Is there going to be top players coming to Tottenham to play with him? Or is he going to have to go elsewhere to play with top players?”
Despite failing to win a trophy so far in his career, Kane has still seen significant progress made both on and off the pitch at Spurs, with the club having reached the Champions League final for the first time in its history last season while also moving into a new state-of-the-art stadium.
“At the moment I would say his career at Tottenham,” Sheringham added. “I know they haven’t won anything – but the career has been steadily going forward, but I think it might be at a crossroads, and if not this year, if they haven’t won anything or don’t look like they’re going forwards in the next season I think there could be changes because Harry’s only got one career and he wants to win things.
“My advice would be, you only get one career Harry, make sure you make the most of it.”