Mauricio Pochettino asked whether there was a better centre-forward in world football than Harry Kane after watching him inspire a 5-2 rout over Southampton with a record-breaking hat-trick.

Kane will finish 2017 with 39 Premier League goals – eclipsing Alan Shearer’s record from 1995 – while his tally of 56 for club and country during the calendar year makes him the leading scorer in Europe, ahead of Barcelona’s Lionel Messi.

Kane has made plain his determination to one day rival Messi and Real Madrid’s Cristiano Ronaldo as the world’s top player and he has achieved that over a remarkable 12 months – during which he has scored eight hat-tricks.

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Pochettino said that Kane belonged in the most illustrious of company and, when making comparisons, the Tottenham Hotspur manager wondered whether there was a more lethal No9. He does not consider either Messi or Ronaldo to be pure centre-forwards.

“Harry is world-class,” Pochettino said. “Of course, Messi and Cristiano are different. Today – one striker in the world, a specific position – who is better than Harry? It’s difficult to say he’s the best but he’s shown to everyone he’s one of the best. Both of his records are massive – to break the Premier League record set by Alan Shearer and then, if you see that over the last seven, eight or nine years, it’s always Messi and Cristiano and now, it’s Harry as well.”

Pochettino noted that a big part of Kane’s challenge now was to maintain his level; to reproduce these numbers over a period of years. “Becoming better may be a very small step of improvement but when you are at this level, you need to fight with all your determination to keep at this level,” the Argentinian said.

“To do this, you need to work hard, more than before, be more professional and more focused. If you achieve something and you say: ‘If I need to run 10 metres but I will run only nine,’ you will cheat yourself, and that is a massive problem.

“The most important thing is to keep the same mentality. The secret is to work hard every day. You cannot say no for one day. That is the secret of the big players like Harry, Cristiano and Messi. You cannot afford not to work every day.”

Kane promised to take his team-mates for dinner to thank them for helping him to his latest landmarks. “It was hard not to think about the records today and I’m very proud of them,” he said. “Messi and Ronaldo have dominated football for so long and they’re two of the greatest players ever so it’s an honour to even be compared to them.

“I’ll keep working harder. It’s about finding little per cents to get better and doing things on the training ground to make you better. How have I improved this year? I’d say physically, recovery from games, eating right and looking after my body. We have such a busy schedule but I feel sharp and I feel at my best. I’m getting more experience.”

Mauricio Pellegrino did not use Virgil van Dijk for the third game in succession and the Southampton manager offered no assurances that the defender would be at the club after the January transfer window. Van Dijk pushed for a move to Liverpool last summer only to see it break down and he has now been linked to Manchester City.

“We have to wait until January,” Pellegrino said. “I can’t control the market. Virgil is part of our club and he’s an important player for us but we’ll see what happens.

“Manchester City? I can’t control the whispers and news from outside. We tried to do the best for the team [last summer]. The board decided to try to keep our best player at the club. This situation is a big learning curve for everybody and now we decide what is the best for the club.”