But the 22-year-old, whose side host Chelsea in the Barclays Premier League on Sunday, insisted earlier this week that he would not be distracted by such talk.
He has again stressed that stance, vowing to remain at the Emirates Stadium to repay the faith shown in him by Arsene Wenger and to be successful with the north London club.
"I am so happy here," he told the Daily Mail. "And I want to continue to be part of what is happening here. Definitely.
"If not, I would have left when I had the opportunity, three years ago, two years ago or last year.
"I believe in this team and I feel we can achieve things. The boss believes in us more than anyone, and I feel I am part of it. He makes me see that as well. And I don't want to fail here."
Fabregas likened his situation to that of Liverpool skipper Steven Gerrard, who appeared on the verge of joining Chelsea four years ago but opted to remain at Anfield.
"I think you have to be grateful to those who have helped you," the Spain midfielder continued.
"When Steven Gerrard had the opportunity to go somewhere else he chose to stay with the club of his life, and I don't think he will ever regret that.
"He made a decision to stay and he has to believe that it was the right one."
Fabregas, meanwhile, is relishing his position as a senior figure in the Arsenal set-up and feels he has grown into the role of captain.
"I don't feel like a normal 22-year-old," he said. "This is my seventh season at the club and my sixth season in the first team.
"In the case of most 22-year-olds, a bad game would be put down to their age. But if I have a bad game, or Arsenal lose, I know I am the first to blame.
"But I like that. I like the responsibility and the pressure. I don't want to be your average 22-year-old.
"I was only 21 when I was asked to captain this club. I had my doubts about whether I could do it at the time. But now I feel very comfortable being captain. It's not even something I think about."
Arsenal v Chelsea 1st Goalscorer: Fabregas, C. 9/1