He has subsequently established himself as one of football's most influential midfielders and, as a result, has regularly been linked with a return to his old club.
Real Madrid are also admirers of the 22-year-old, but Fabregas has no intention of seeking a move back to Spain.
"We don't need to talk about my future," Fabregas told the Daily Star Sunday. "I don't understand all the rumours about me.
"I've always said that I'm happy at Arsenal. I can say a thousand times that I won't go to a Spanish club, but nobody believes me.
"Arsenal is my home and I don't have any plans to leave."
Meanwhile, Fabregas is relishing the Champions League quarter-final dates against Barca, with the holders due to visit Emirates Stadium for the first leg on Wednesday.
"I know they will be two exciting games," added Fabregas, who is battling to overcome a knee injury picked up in Saturday's 1-1 draw at Birmingham City.
"We will, of course, give everything, and you know if you want to win the competition, you have to be ready to play anyone.
"The last round of the Champions League was interesting and it shows you can never underestimate any opponents in this competition.
"It should be a warning that any team left in can beat anyone else - even if the reputation is lower maybe than Real Madrid, Chelsea or Liverpool, they can still win."
Arsenal Stage of Elimination Stage Of Elimination: Winners 9/1