The London club have had a bid accepted by Bolton for England defender Gary Cahill, but personal terms are still proving a sticking point.
Speaking at Monday's William Hill Scottish Cup draw in Glasgow, Villas-Boas said: "Apart from a central defender, we might get one more player in but we're not sure yet.
"It's always difficult. The top talent is normally cup-tied in the Champions League or in different domestic competitions and it's difficult for the selling club to make players available.
"It's normal that you struggle in the transfer market.
"Normally it's a market where you overpay a lot and that's what we don't want to do now.
"That's why we have set out not to do a lot in the transfer window."
Chelsea defeated npower Championship outfit Portsmouth 4-0 in the third round of the FA Cup on Sunday.
They could now face west London rivals QPR in the fourth round, assuming Rangers can defeat MK Dons in their third-round replay.
Villas-Boas believes the sacking of Neil Warnock as manager of QPR has again highlighted the pressure bosses are under in the Barclays Premier League, with the Portuguese's future having been in the spotlight earlier this season.
He said: "It's always sad news. The Barclays Premier League is always intense and very media-hyped, pressure is all over the place.
"You are expected to get results and you also need people to trust in you when you take a challenge of that dimension in your hands.
"Neil did a fantastic job with QPR bringing them up to the Premier League.
"This was a decision that was taken by Tony Fernandes, the owner, and he is the one who has to decide ultimately what he wants for the future of the club and he decided like that.
"I don't have the power to make any negative critique on his decision because it has nothing to do with me.
"Just the fact that we lose a manager shows there is a high demand for us to get results and it's ever-present in the Premier League."
Florent Malouda has rejected the notion that Chelsea are in a stage of transition and believes fortunes will soon change.
The west Londoners have endured a turbulent season since Villas-Boas was appointed in the summer.
Adjusting to life under Villas-Boas has been cited as a cause, but Malouda feels performances have just not been good enough.
"I don't like this expression of transition," he said.
"When you play for Chelsea there is no transition because everyone expects the best from the squad we've got. There is a lot of talent and ambition.
"When you sign for the club, it doesn't matter who the players or manager are, all you expect is to win trophies. There is a mentality here.
"I think that's what the fans expect from us as well. We should not look at all the changes as an excuse, we must contend to win trophies year after year.
"The newer players have settled very well in the team. Everyone is focused on the club objectives and are sad when we don't have the results we expect.
"We're always trying to turn things around and we know how fast things can change.
"We know when we don't have results, doubts are coming from the outside so we have to stay strong as a squad to be able to compete for trophies. We have to go for it."