Under Pochettino, Spurs have qualified for the Champions League for three seasons in a row while operating on a smaller budget than rivals such as Manchester City, Manchester United, Liverpool, Chelsea and Arsenal.
Up until now Pochettino has largely played by Levy's rules and accepted the club can not afford to compete with their top-four rivals.
"If we want to be real contenders for big, big trophies, we need to review a little", Pochettino said, according to the BBC. A few weeks ago, the Argentine questioned his own future at the club, as if he couldn't achieve all he wants to in North London. "Mentally that's a big step we need to go forward".
While he Blues still have the FA Cup final on the horizon, they have missed out on a Champions League place by finishing fifth in the Premier League. Are Spurs going to be able to catch them? Until today it was so hard to talk about the future.More news: North Korean delegation visits China
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If the deal is completed, Hysaj would become the seventh most expensive defender of all time - a reward for his impressive form as Napoli fell just short of the Serie A title.
In his pre-match press conference ahead of the Leicester game, the ex-Espanyol boss said "today it is 100 per cent (I stay) because I have a three-year contract here". I think the style of play is something that suits me and the players we have.
"In football, you never know", he replied. Obviously it's been long rumoured Chelsea are going to change manager too... but in reality I'm not sure Pochettino would make that move.
"You need to give your best every day and you need to work always with this fear you can lose your job if you're not professional and if you don't work 12 hours a day".
Jose Mourinho is expected to strengthen his squad in order to try and compete with Man City next season and Alderweireld would be a significant upgrade on the likes of Phil Jones and Victor Lindelof.