Fabregas has long been linked with a return to Barca, the club where he learned his trade as a youngster before moving to the Gunners seven years ago and the Catalan giants had a £29million (35million euros) offer for the Spain international rejected last week.
Reports today suggested Arsenal are now prepared to accept an offer - if Barca increase their bid to £58million (70million euros).
However, Oliver insists they have heard nothing from the Premier League club.
"They said they would not sell, it's logical therefore that they have not set a price for him," he said as he left a Barcelona board meeting.
"We made a formal offer. The only official response we have from Arsenal is that they are not ready to sell the player, for which it would be difficult for them to be putting a price when they say they are not selling."
Oliver was keen to remind the public that in Barca's favour is Fabregas' "desire to come" and claims the 23-year-old "would want to sort it all out" as soon as possible.
He claims Barca are ready to complete the deal immediately but admits it will be impossible without either the green light from Arsenal or Fabregas forcing his club's hand.
"On our part, after having made an offer we are ready to sign the deal this very morning," Oliver continued.
"We still have time to do it, but it is a deal we can not do just by ourselves."
The 23-year-old is under contract to Arsenal until 2015 but last month reiterated his desire to head back to Barca.