The Brazilian suffered knee ligament damage during last weekend's 0-0 draw at QPR, and has since undergone surgery that will see the 23-year-old miss the remainder of the season.
Despite losing such an influential player, Villas-Boas has said he will stick with the midfielders he currently has at the club, with Jake Livermore's potential loan-move to the Hoops now seemingly in jeopardy.
"The only thing we have done at the moment is hold on to our midfielders, the ones who are here," Villas-Boas said.
"We have put on hold the movement of Jake Livermore's possible loan to another club. It is not out of the question, I think we are still pretty happy with what we have.
"We have to be careful. We still have a couple of weeks before the market closes, so we have to be careful with the decision and it will be something we hold on to and see how we go."
When asked if he was lining up any new arrivals the Portuguese replied: "It is not impossible but it is unlikely. At the moment there is nothing."
England international Scott Parker is the likely replacement for Sandro, with the former West Ham skipper only just returning from an Achilles problem.
The 32-year-old has not started a Premier League game since April but has returned in recent weeks.