The Belgium international is out of action with an ankle injury sustained on national team duty at Euro2016 which is likely to keep him sidelined for the start of the new Premier League season, kicking off on August 13.
Vertonghen and fellow Belgian Toby Alderweireld are both in London preparing for the return of the Spurs squad, who are in Melbourne for the International Champions Cup, but there will be no issues in the North London club's central defensive stocks according to the boss.
"He is very close to coming back.
"We have enough players in the position."
Quizzed further on Vertonghen, Pochettino admitted he was unsure if the 29-year-old would be available for the season opener against Everton at Goodison Park.
"We will see. He is going well in the last few days but we will see when we arrive (in London) on Monday what condition he is in," he added.
"For the start of the season we have enough players in that position."