Speculation has long linked the Arsenal captain with a return to the Catalan club, where he spent several years as a youth player before moving to north London.
Barca star Lionel Messi was today reported as saying he believed it was just a matter of time before Fabregas returned to the Nou Camp as he "has Barcelona in his blood", but Hill-Wood is convinced a deal is not in the pipeline as the Spanish champions are happy with their current crop of players.
Hill-Wood revealed that high-level talks between the clubs during their recent Champions League tie ruled out the possibility of Fabregas joining up with Pep Guardiola's side any time soon.
"There was a private conversation that took place in the boardroom and assurances have been made at the highest possible level," Hill-Wood told Soccernet. "Arsenal do not expect those to be broken.
"I was not privy to the conversation, but was told about it. They said to us they are not interested [this summer]. It was a recent conversation, as recent as the time that they played us in the Champions League in fact as we got a bit upset because of all the media speculation.
"Subsequent to the conversation, if they are interested at any time in the future, they would come to us direct. However I'm not sure they are going to do that, because they told us they are pretty happy with what they have got and are pretty happy with their current players."
However, this summer's presidential elections mean the Barca hierarchy is set to change completely before the transfer window closes and could render such assurances meaningless.
Hill-Wood also stated his belief that a move to the Nou Camp could be a bad move for Fabregas, with star duo Xavi and Andres Iniesta so pivotal to Barcelona's play in the middle of the park.
"If you want my opinion, I'm not sure he would even get in their team," he said. "Do they need him? I'm not sure that they do. And they said to us they are not interested.
"That suits us fine. Fabregas is an Arsenal player and we want him to remain an Arsenal player. We hope he stays with us for a very long time."