The former Spurs forward believes the England international is in the best place for his ongoing development and should ignore all exit talk.
As a former Spurs goal-getter himself, Sheringham knows all about the pressure of being a star turn at White Hart Lane.
As a man who also swapped north London for Manchester United when at the height of his career, he will also understand how difficult it can be to ignore mounting transfer talk.
Kane has, however, offered no indication that he is looking to move on any time soon, with there a realisation on his part that he still has plenty of hard work ahead before he can consider himself to be a top Premier League and international performer.
His efforts in 2014/15 drew plenty of praise, as his breakthrough season at the highest level delivered 30-plus goals and senior England recognition.
It is those efforts which have sparked speculation regarding his long-term future, but Sheringham believes the 22-year-old is in the best possible place at this stage of his career and should continue to turn a deaf ear and blind eye to any potential distractions.
Speaking to 888sport.com about Kane and the decision to stay put for now, Sheringham said: “He’s at where he’s at and that’s a very sensible decision to take at the moment. He should be honoured still to play for Tottenham - and the way he speaks he is. He’s loving every minute of it so he hasn’t got eyes for anyone else.”
The now Stevenage manager is also convinced that Kane can kick on this season and build on his heroics efforts from 2014/15.
He added: “When you have the qualities Harry has I’d thoroughly expect him to do exactly what he did last year. I don’t think he’s a flash in the pan or a one-season wonder. I really think he’s the real deal and wants to learn and if it doesn’t come as easy for him as last year he’ll find a way to do it in other ways.”
Kane will be looking to open his account for the new season on the opening weekend, and that quest will take him to Old Trafford for a meeting with United on Saturday.
Spurs will be looking to him to lead the charge across the course of the campaign, with Mauricio Pochettino yet to bolster his attacking options – although there is still plenty of time left in the summer window for additions to be made, especially if a few of those deemed surplus to requirements can be moved out.