The Brazil international handed in a transfer request earlier in the season after becoming surplus to requirements at Stamford Bridge, and is widely expected to leave the club in January.
QPR have recently appointed Mark Hughes as manager and owner Tony Fernandes has stated that the Loftus Road outfit will be busy in the transfer window.
Although not naming the team who have been in contact, Villas Boas has spoken of the bid for Alex’s services.
“From what I know from my chief executive, there has been an approach from a Premier League club,” the Portuguese trainer told The Telegraph.
“We have respected Alex’s transfer request so the market’s open for him.
“We’re just trying to reach the level of proposal we think is good for the player. Nothing has happened up to now, but we’ll listen to all offers.
“We’ll present anything to the player. He has to make a decision. He has generated interest from a lot of clubs,” he commented.
Meanwhile, Villas Boas also stated that a move for Bolton defender Gary Cahill should be completed in the near future.
“There is no real news and the negotiations are still ongoing.
“That doesn’t mean we don’t want it solved as soon as possible. We’re making good, solid progress. Hopefully it can be concluded soon and he will be a Chelsea player.
“It’s all part of negotiation. I’m sure all parties are protecting their interests and we’ll reach an agreement. I think soon.
“I feel it’s unfair for me to put the reasons for the delay into the public eye. The delay isn’t a negative. It’s just something that’s happening.
“It should be concluded soon and that’s a positive. Hopefully we can reach an agreement. It’s part of business. I’m okay with it.
“But we kept a couple of other options available and we can act quickly if that’s the case. But I’m pretty confident it will happen,” he concluded.
By Gareth McKnight