The Daily Star says the Gunners have rejected Barcelona's opening £30m offer for Fabregas - and told the Spanish giants to come back only when they are serious.
An Arsenal club source says a verbal £30m offer from the European champions had been turned down.
But the source added: "There was an offer and it has been turned down flat.
"They have been told to come back when they are serious with a proper offer and we will consider it."
Barca have been told by Arsenal that they want £60m for club skipper Fabregas.
In reality they would be prepared to accept something in the region of £40m-£45m because they know the Spanish midfielder wants to quit the Emirates for his boyhood heroes.