After spells on loan at Leyton Orient, Millwall, Norwich City and Leicester City, Kane turned down another temporary move last summer in order to fight for his place at Tottenham.
His decision to stay has paid off after Kane became the first Spurs player since Gareth Bale to score in three successive matches with his strike in a 3-1 derby win over Fulham.
And Kane hopes he can emulate fellow east Londoner Sheringham and carve out a successful career for himself at White hart Lane.
"He's a great finisher and was very good at getting in the box, scoring so many goals, especially for Spurs," Kane said.
"As I grew up I tried to use him as a role model and if I can score as many goals as he did, it would not be bad.
"I met him once at a golf charity day and got to talking about Millwall [one of Kane's loan clubs] because he played for them as well. It was great to meet him."
Asked what advice Sheringham gave him, Kane said: "Just to score goals. As a striker you have got to score goals.
"It was only last year - we had a little chat about football. He's a great bloke and it was nice to meet him.
"I was a little bit star-struck, to be honest. When you meet your idol you don't really know what to say but he had great conversation."
The 20-year-old also revealed he hopes his new-found success can inspire the next generation of English talent.
"When you saw a young English talent coming through the ranks you wanted to aspire to that. Hopefully young kids can do the same (with me)," he said.
"People recognise me a bit more because I am at the top level and scoring goals. People want your picture and stuff but I am happy because I was a fan once."