The 20-year-old Spain midfielder has chosen to stay at the Emirates Stadium despite interest from Real Madrid, and he feels the club has a chance for success this season despite the loss of Thierry Henry to Barcelona.
Gilberto Silva is the current captain following Henry's departure but Fabregas admits he would eventually like the armband.
"Everybody wants this kind of responsibility and 100% me as well," he said. "It's something that I have liked ever since I have been young and it would be no problem for me to be captain of this club."
Fabregas is confident Henry's departure will not be affected next season, although he admits the France forward will be missed.
"Thierry has been really, really important to this club over the past eight years," he said on the club's website. "We have scored a lot of goals because of him but now he is gone and we have to move on. We wish him all the best at Barcelona.
"The future is looking good. We have very good young players and most of them are teenagers. We are all ready to fight for the League, the Champions League, the FA Cup, the Carling Cup, for everything.
"We must fight for everything that is in front of us. We must prove we are not just young but that we are winners."