Kane moved to within 60 goals of Shearer after scoring his 200th in the competition against Manchester City on Sunday.
The 29-year-old in the process joined Shearer and Wayne Rooney as the only players to score 200 or more Premier League goals.
Unlike Shearer and Rooney, Kane, who surpassed Jimmy Greaves' record of 266 goals in a Spurs shirt with his strike against the champions, is yet to win a Premier League title or any trophy for that matter.
Nonetheless, Shearer is optimistic his long-held record is now in sight for England's captain.
"I'm cool with it," says Shearer in an exclusive interview with the Premier League.
"I know how much he wants it - he's told me - which is fine, because I was exactly the same.
"If he stays fit and stays in this country then he'll do it. It's just a matter of when. He's doing what great goalscorers do, and there aren't many better than him.
"First and foremost, he's the third player to get 200 goals. Only myself and [Wayne] Rooney have done that, so it's a small club.
"His form is as good as ever. His team's not doing as well but his stats, that doesn't seem to be affecting him at all.
"He had a huge disappointment at the World Cup but I think he's come back mentally stronger than ever, and that doesn’t surprise me. I'm a huge fan of his. He’s a fantastic player.
"I've had it [the record] for such a long time that I've always said it'll go one day. I thought Rooney might have a great chance of doing it. Obviously he slowed down and then went over to America.
"It's going to go one day, so if it goes [to Kane] then I'll be the first to shake his hand."
"We're slightly different players in terms of what he can do and what I could do," he says. "He [Kane] doesn't mind dropping deep and playing the No 10 role, whereas I always wanted to be as far forward as I could.
"But in terms of the attitude to scoring goals, that's similar. I can see his thirst, his desire and hunger, to just score as many goals as possible. He doesn't care how they go in.
"All great goalscorers have that belief, that sense of arrogance or confidence. He's a phenomenal player, a master of what he does, and his hunger for goals is as good as ever."
