The 26-year-old was given a spell on the sidelines after suffering an ankle injury during Tottenham's 3-1 defeat to Sunderland in the Asia Cup on July 24.
Despite manager Andre Villas-Boas claiming that Vertonghen is likely to miss the club's first competitive clash against Crystal Palace at Selhurst Park on August 18, Vertonghen is hoping for the best.
"I'm making a lot of progress," Vertonghen told Sky Sports News. "I'm starting to run. The next game is nine, 10 days from now, so I will be quite close. You never know what can happen and I always aim for the best and hope next week I'll be very close."
Meanwhile, it remains unclear whether Spurs will begin the season without prolific winger Gareth Bale, who could make a world-record transfer to Real Madrid.