Spurs chairman Daniel Levy wants the 62-year-old to take over from Tim Sherwood after the World Cup but Van Gaal has been considering his options having been linked with Manchester United.
Van Gaal has long been considered the favorite to take over in the summer but Tottenham is now waiting for an answer from the Dutchman as the club actively searches for a replacement for Sherwood.
Southampton boss Mauricio Pochettino is under serious consideration as an alternative to Van Gaal and will delay talks over a new contract with the south coast club until the end of the season.
But Levy wants Van Gaal, who will step down as Netherlands coach after the World Cup and has made no secret of his desire to manage in the Premier League. The pair met following the dismissal of Villas-Boas in December but the former Bayern Munich and Barcelona boss refused to split the Spurs job with his Holland duties.
Spurs are now sweating on Van Gaal's decision amid concerns he is holding out for a chance to manage United after reports of a meeting held last week with Old Trafford chiefs about the possibility of taking over from David Moyes.
Spurs chiefs have been worried about feedback about the Dutchman’s abrasive character but there is a recognition at White Hart Lane that the club cannot pass up the opportunity to appoint a managerial legend who has won titles in Holland, Spain and Germany.
Van Gaal is also an attractive proposition because his arrival would not require Spurs to pay any compensation as his contract with the Dutch FA expires after the World Cup in Brazil.
If Van Gaal delays for too long, he could miss out on the opportunity to manage Tottenham.
Pochettino is well aware that he is highly rated by Levy and expects an interview to press his claim to take over from Sherwood, who was told last week that the club would be making a change just four months after his appointment on an 18-month contract.
The Argentine, 42, has a year left on his Southampton contract and has so far refused to sign a new deal, with the club expected to sell key players this summer, including Luke Shaw and Adam Lallana.
Pochettino would fit in to Tottenham’s continental management structure which includes a director of football and a committee responsible for identifying transfer targets, with the ‘head coach’ asked to focus on first-team performances and results.
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