The Welshman limped off during last Saturday's victory at Fulham and will sit out this weekend's fixture at Goodison Park but could be back on 16 December.
Villas-Boas said: "He will not make Everton but could be back for next weekend. But I have other options and I have excellent players."
Midfielder Scott Parker has yet to feature for Spurs this season while full-back Benoit Assou-Ekotto has also been a long-term absentee but the duo may also be back in the squad for the Swansea match.
Villas-Boas said: "It is ever so close for them. Maybe not this week, but maybe next Sunday against Swansea. However, they have both been out for some time, so we have to be sensible with the situation.
"Parker is an amazing player and it is a big boost for us. He is an exceptional player and it means more competition for places.
"We haven't been able to rest as much as we wanted, so the more options the better for me. More headaches for the manager but we are very grateful to see him back.
"He is focused on getting back and that is his big motivation at the moment. He wants to be part of the team and I'm sure he will be part of the team. It is not even a consideration."