Arsenal chairman Peter Hill-Wood has confirmed that although Barca have made contact with the Gunners regarding Fabregas, a formal offer for the player has not been received.
"Yes, they have spoken to us about Cesc," he told The Mirror.
"They have been in touch. But so far they have not made a bid and we do not want to let him go.
"But he comes from Barcelona so it is understandable if he wanted to go back. However, they have not made an offer so far."

The reigning European and Spanish champions had a €40 million bid for the 24-year-old midfielder rejected at the start of last season and maintain they will not up their valuation of the player.
For their part, Arsenal insist they are not interested in selling Fabregas who appears happy to stay on at the North London outfit for one more season.
What is clear is the longer Barca wait to make an offer for Fabregas, the less chance they will have in landing their target. The Gunners are not in dire straits financially and will certainly not want to lose a key member of their squad when there is not enough time to find an adequate replacement.
Fabregas came up through the youth ranks at the Catalans before moving to Arsenal in 2003.