Fabregas has been linked with a move back to the Nou Camp for the last two seasons and after the Gunners failure to win any silverware, could the midfielder be tempted to go back to the club he joined as a youngster.
The Spanish giants remain keen to sign Fabregas and are ready to make a new move this summer, although Hill-Wood insists they have yet to make a bid for the 24-year-old.
"Yes, they have spoken to us about Cesc," said Peter Hill-Wood.
Arsenal’s chairman also added; "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."
Arsenal are expected to be busy in the transfer market this summer and Hill-Wood insists Arsene Wenger will have funds to spend.
"There is money for the manager," added Hill-Wood.
Will the Gunners ace head back home?
