The 21-year-old striker has risen to prominence this season after finding the net with regularity, scoring 24 goals in 38 appearances in all competitions.
His stock has risen further following goals against the likes of Chelsea, Liverpool and North London rivals Arsenal, and many observers around White Hart Lane are already drawing comparisons with club greats.
Former winger Anderton feels such parallels are unfair on Kane as they draw added pressure, however he does concede that the young striker has similar traits to club hero Sheringham.
"It was that header that beat Arsenal," Anderton says. “It had Teddy written all over it, easing on to the shoulder of the defender, climbing, heading the ball back across goal to where it was coming from.
"Massive game, big moment. He just made it look so easy - such a class goal. I watched it and went: 'Yep, I've seen that before.'
"It's not really fair to call him the new Teddy Sheringham because that's so much pressure to load on a young boy, and Harry looks as if he will be very much his own player.
"But there are similarities because in both cases they offer the complete package.”
Too much pressure?
Spurs striker Kane has rightfully taken the plaudits this season, not just through his incredible goal scoring form but also his ability outside the box and his willingness to work hard for the team.
However, too much praise, building him up and comparing with former greats such as Sheringham and Alan Shearer, will only add to the pressure to maintain or even improve his current standard.
Aside from the extra pressure, the Lilywhites and the White Hart Lane supporters must refrain from placing too much hope on him and begin to set unrealistic demands.
The next step in his progression is England recognition, but Kane is his own man, with his own style and he will need encouragement and not added strains in order to reach the top.