However, Fabregas has been quick to refute the notion that he could be set to leave the Camp Nou and move back to Arsenal.
"It was a privilege for me to spend eight years at such a magnificent club," Fabregas claimed of his time at Arsenal, in an exclusive interview with the Sun.
"But now is a new chapter at Barcelona and I said when I signed here that it was going to be the most exciting and difficult challenge of my life.
"I knew I was coming to compete for a place against the best players in the world. But I like big challenges.
"If I didn't I would have stayed at Arsenal where I was the captain, where I played every game and where I was treated so well.
"I have a big heart, a strong character and I have the courage to carry on competing for my place."
Fabregas also claimed that he expects Arsenal to challenge for the Premier League title this season. The Gunners blasted Southampton 6-1 on Saturday to give them eight points from four Premier League matches with just one goal conceded to date.
The form of Arsene Wenger's side has been a welcome boost to Arsenal fans, many of whom were pessimistic following the departures of Robin van Persie and Alex Song and the subsequent failure of the Gunners boss to add to the squad.
But Fabregas, who left Arsenal for Barcelona last summer, said that he always had faith in his former mentor, Wenger.
"Arsene Wenger is amazing and I'm sure he will prove it again this season," the 25-year-old explained, according to the Sun.
"He always finds the best young talent in Europe and has the courage to bring them in and give them their chance.
"That is his special talent, the way he works with a player to build their confidence and encourage them to play, to perform at their best.
"That's why I'm confident that Arsenal will again be up there challenging."
While Olivier Giroud has thus far struggled since his move from Montpellier, fellow new signings Lukas Podolski and Santi Cazorla have looked the part early in their Arsenal careers. Cazorla has particularly caught the eye in helping provide the creativity from midfield that has largely been lacking since the departure of his former Spain international Fabregas.