With Real Madrid desperate to sign Kane, who has also been named the Premier League's December Player of the Month - Pochettino welcomed Levy's words about key players staying, even if Spurs fail to qualify for next season's Champions League.
Tottenham Hotspur striker Harry Kane became the London club's top Premier League goalscorer with 98 goals after his second-half brace helped the hosts thump Everton 4-0 at Wembley Stadium on Saturday.
In this way he will break all the records in the Premier League.
Having already beaten Alan Shearer's calendar-year record for the most Premier League goals (39), the England worldwide also has two successive Golden Boots and has just equalled the all-time record for the number of Premier League Player of the Month awards, as his sixth has taken him level with Steven Gerrard.
Pochettino said: "He is fantastic and he deserves all the credit and all the praise, so I want to congratulate him one more time".
"He can do anything because of his mentality and how professional he is".
"It is unbelievable the way that he is able to work and his willingness".
Upon scoring his second in the 4-0 win, Kane became just the third player to score at least 20 Premier League goals in four consecutive seasons, after Thierry Henry (five) and Alan Shearer (four).
Heung-Min Son put the home side ahead in the 26 minute when he tapped in Serge Aurier's low cross.
"It's something I'm very proud of but it's on to the next one, just keep going and these boys are great at setting me up", Kane toldBT Sport. "Hopefully I'll keep scoring".
Tottenham are now unbeaten in six matches.
With 22 minutes on the clock, the visitors thought they had taken the lead when new striker Cenk Tosun headed on a corner and Wayne Rooney pounced, only for him to be flagged for offside. Allardyce felt Kane's opening goal could also have been ruled out.
Doucoure turned the ball in with his hand as he stooped for a header but, with no video assistant referees in the Premier League, the goal stood and denied Southampton a first league win in 10 games.
"Or what would the game have gone like if Harry's goal would have been disallowed - because I think it's offside looking on the laptop".