Spain international Fabregas is understood to have told the Gunners last week that he wants to rejoin former club Barcelona after spending seven years in London.
Barca have confirmed an interest in signing the 23-year-old, but have insisted they will be respectful towards Arsenal during any negotiations.
Hill-Wood says he is yet to hear from the La Liga champions and has reiterated his stance that he is not looking to encourage offers for the Gunners captain.
"We have heard nothing at all and I am not looking for a telephone call from them," Hill-Wood told the Daily Star. "As far as I am concerned, he is our player. If they want to make a bid it is up to them."
Regarding the lack of approach, Hill-Wood added: "We are very surprised, but delighted."
Reports have claimed that Arsenal have placed an £80million price tag on Fabregas, who is currently recovering from a cracked fibula in time to be fit for Spain's World Cup campaign.
The Catalan giants' director general Joan Oliver claims, however, that a tentative enquiry has been made with their Premier League counterparts as Barca weigh up their next move.
"There is no offer yet," Oliver told the club's official website.
"It's true the player has expressed his wish to play for Barca, perhaps this coming season.
"We have had first contacts with Arsenal in which we made known our intention to talk and that's the current situation.
"We are not in any hurry and you never know how long these operations can take."