Reports have claimed the bidders are west London rivals QPR, whose new manager Mark Hughes on Wednesday indicated his interest in the Brazilian.
Villas-Boas said on Thursday afternoon: "From what I know from my chief executive, there has been an approach from a Premier League club.
"It is a player who we have accepted a transfer request for, so we have to listen to offers."
Chelsea are planning to replace Alex with Bolton's Gary Cahill, who they have struggled to agree personal terms with.
Villas-Boas insisted he had set no deadline for a deal to be concluded and but was hopeful that would happen before the end of the week.
"Still an ongoing negotiation, not that we don't want it resolved as soon as possible," said Villas-Boas, who refused to criticise Cahill or his representatives over the player's wage demands.
"I'm sure that all of the parties are protecting their interests."
Villas-Boas denied that Chelsea had made a reported £25million bid for Lille star Eden Hazard but admitted he was a fan of the player.
The Blues boss confirmed Josh McEachran would go out on loan for the rest of the season - ostensibly to Swansea - after Saturday's game with Sunderland.
He also said Gael Kakuta's loan move to Dijon had not been concluded yet but expected it to happen "soon".
The French club have announced the move on their website, but it is not yet finalised.
Meanwhile, Florent Malouda is a doubt for the Sunderland game after failing to train for the last two days.