Kane's treble at Turf Moor on Saturday took his Premier League goal tally in 2017 to 36.
His manager Mauricio Pochettino believes he cannot only reach that goal but has the capacity to get even better in the coming years.
- Kane's third goal against Burnley was his 46th club strike in all competitions in 2017; only Edinson Cavani and Lionel Messi (50 each) have more among players in the big five European leagues.
Harry Kane stole the show once more, scoring three and threatening throughout, and the Spurs boss mentioned how he sees the England forward surpassing Shearer's Premier League goal scoring record in the very near future.
The good thing is that mentally as a group we know that every game is a challenge for us and I think that there is an acceptance of that and there's a reality to it.
The legendary forward posted 36 emojis on Twitter and added: 'Congratulations Harry Kane!'
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But with 68 minutes played, Spurs at last doubled their lead. "I'm anxious when you don't create chances though", he said.
Following today's win, Kane said: "A few people have been speaking about it".
"During my three and a half years with Tottenham, he always surprises me - not only with goals but his contribution, with his attitude, professional ethic, how he works across the pitch, he is a massive example for everyone", he said.
He now shares that record with Newcastle and Blackburn icon Shearer and will attempt to create history against Southampton after Christmas.
The 24-year-old broke the deadlock in the sixth minute from the spot, after Dele Alli was bundled over in the box by Kevin Long - although Clarets fans hounded the England man for the remainder of the game for an alleged dive.