The defender, who missed Tottenham's 2-1 Premier League victory at Sunderland on Saturday with the ligament issue, is expected to be sidelined until the new year.
However, head coach Villas-Boas claimed the club would employ a blood-spinning technique to avoid Vertonghen requiring surgery.
"At the moment there is ankle ligament damage," he said. "We will have the player in a boot for one or two weeks to try and settle it.
"We want to - and we will - avoid surgery on the player.
"We will use PRP treatment to try and get him back as soon as possible. We've had outstanding results with PRP treatment and we will do that with him."
Villas-Boas also vowed to maintain his rotation policy as Tottenham takes on Anzhi Makhachkala in its final Europa League group-stage clash on Thursday.
"We've made a lot of changes in the Europa League fixtures so far so we will keep that," he continued. "Giving opportunities to players in this competition [on Thursday] will put them in contention for the game against Liverpool [on Sunday].
"We will use, as much as we can, the possibility of rotating the players, giving others a rest, bearing in mind we are qualified first."
Tottenham has already made it through to the knockout stages of the competition having won all five of its Group K fixtures so far.