They are in second place, seven points behind Leicester with five games remaining, and have the best defensive record and best goals tally in the league.
Pochettino's style of play and willingness to push through young players into the first team has caught the eye of clubs at home and across Europe.
Vertonghen, who returned in the 3-0 victory over Manchester United at the weekend, said Tottenham must resist any attempt to lure him away.
"For me it is vital. To keep this thing going, he has to stay," the Belgian told British media.
"I think everyone wants him to stay and he feels that -- we want to fight for him and that this team is the best thing for him, so I hope he stays."
"I am extremely excited. If you feel the buzz in the club, in the dressing room with the guys, it is something I've never experienced before and we have to keep this together. It is something special," he added.
Tottenham travel to face Stoke City at the Britannia Stadium in the league on Monday hoping to keep the pressure on Leicester and keep alive Tottenham's hopes of a first title since 1961.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Martyn Herman)
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