The Gunners have been angered by constant reports from Spain that the European champions want to bring Fabregas back to the club where he started his career.
And Hill-Wood has revealed that a high-level secret meeting between the two clubs was held when they met in the Champions League quarter-final.
Give up the chase: Fabregas takes on Barcelona at the end of last month
Committed: Fabregas kisses the Arsenal badge after scoring against Blackburn Rovers
'There was a private conversation that took place in the boardroom andassurances have been made at the highest possible level,' Hill-Woodtold EPSN Soccernet.
'Arsenal do not expect those to be broken. They said to us they are not interested (this summer).'
Emirates boss Arsene Wenger has previously lashed out at how the pursuit has been carried out by leaks to the Catalan media and Hill-Wood admitted that the Gunners confronted Barca about the headlines.
'Subsequent to the conversation, if they are interested at any time in the future, they would come to us direct,' he said.
'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.
'If you want my opinion, I'm not sure he would even get in their team. Do they need him? I'm not sure that they do. We hope he stays with us for a very long time.'
However, the assurances could count for little if, as expected, the Barca board are replaced in the summer.
JoanLaporta has to relinquish his presidency in June and the man currentlyfavourite to replace him is an outsider with links to Fabregas.
Angry: Arsenal boss Arsene Wengerdislikes the way Barcelona presidential candidates like Sandro Rosell(right) can unsettle players
Sandro Rosell is heavily odds on to win the presidential poll and his former role as a Nike director brought him into contact with the 22-year-old.
His closeness to Fabregas and his perceived ability to pull off the signing is one of the businessman's biggest selling points.
Technical secretary Txiki Begiristain, who currently shapes Barca's transfer policy, is also expected to leave along with Laporta.
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