Vertonghen’s current deal expires in the summer of 2018 and the Belgian has been negotiating fresh terms since early this year.
Spurs have already tied seven players down to new contracts since the transfer window closed and Pochettino suggested another is soon to follow.
“In the next few days maybe one more will appear and then we will see what happens,” Pochettino said.
Asked if Vertonghen would be that player, he added: “I cannot give names but maybe yes it is a centre-back.
“All the players that are involved in negotiations it is through the agent but Jan is another player who is in my plans for the future.”
Yesterday, Kyle Walker became the seventh Spurs player to agree a new contract this month, joining Dele Alli, Christian Eriksen, Eric Dier, Danny Rose, Harry Winks and Tom Carroll.
Walker’s deal will run until 2021 and Pochettino believes the recent rush of announcements shows how the culture of the club is changing.
“It is important to keep the key players, always under my judgement,” Pochettino said.
“We sell a lot of players. It is impossible to be all agreed on those but we need to be clear and I need to be clear on my judgement to keep the key players and all the players I believe can be important for the future of the club.
“They need to feel that we are in a project where we can win everything.”
Pochettino is sweating on the fitness of both Mousa Dembele and Dier ahead of today’s trip to Middlesbrough.
Harry Kane’s ankle still remains too swollen to draw any accurate conclusion about the striker’s return but he will have a second scan next week.
It means Vincent Janssen is expected to make his second Premier League start up front at the Riverside Stadium, fresh from scoring his first Spurs goal in midweek.
“Always a striker needs to feel confidence and feel the net,” Pochettino said.
“It is a great opportunity to start from the beginning maybe and help the team.”
Middlesbrough welcome back Cristhian Stuani and Jordan Rhodes, which means Aitor Karanka has only full-back Fabio da Silva and midfielder Grant Leadbitter missing from his squad as he looks to end a run of two successive league defeats.