Hill-Wood also said he did not think a return to Barcelona was in Fabregas's best interest, because of the competition he would face from the likes of Andres Iniesta and Xavi.
"If you want my opinion, I'm not sure he would even get in their team," he stated.
"Do they need him? I'm not sure that they do. And they said to us they are not interested."
Earlier, Barcelona's inspirational striker Lionel Messi fanned the flames of speculation by saying he felt sure he would line up alongside his former youth team colleague again in Barcelona colours at some point.
Messi, 22, played alongside Fabregas at Barcelona's La Masia academy before the midfielder left for north London in 2003.
"Cesc has a place for Arsenal in his heart but he has Barcelona in his blood," Messi told the Daily Express.
"He will want to win the biggest prizes in football and I expect him to do that at Barcelona."
Fabregas is under contract to Arsenal until 2014 and has pledged his future to the club on a number of occasions.
Despite that, he has been consistently linked with a return to Barcelona, the club he joined as a 10-year-old in 1997.
Arsenal boss Arsene Wenger underlined the Spanish international's importance to Arsenal by appointing him club captain in November 2008, having first brought him to the club when he was 15 and overseeing his development into one of the world's most coveted midfielders.
"I don't exactly know when that will be, but I expect him to be my Barcelona team-mate again at some point," said Messi, who scored his 40th goal of the season in Barca's 2-0 victory over Real Madrid on Saturday.
"I am sure that Arsene Wenger and Cesc have a father-son relationship and I know that he has a very special relationship with the Arsenal fans.
"When you grow up at a club, it is more than just a club. The coaches, the players, the people in the club will be like family.
"But Barcelona is his city and it is the club of him and his family. There are only a few players in the world who can improve this squad we have but Cesc is one of them."
Fabregas suffered a bruised bone in his leg in Arsenal's 2-2 Champions League draw against Barcelona at the Emirates in March, putting him out of the return leg in April in which Messi mesmerised the Nou Camp with an awesome individual performance, scoring all Barca's goals in a 4-1 victory.
Wenger afterwards acknowledged Messi as the "best player in the world", while Barca coach Pep Guardiola was equally effusive with praise.
And Messi has no plans to abandon Spain for an English club - or any other.
"Will I play in the Premier League one day? I have said that I want to be at Barcelona for life," he said.
"I will be here for as long as they want me. I owe Barcelona more than for giving me a chance - I owe them for changing my life."
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