The 20-year-old disagrees with former Arsenal stars Thierry Henry and Freddie Ljungberg's claims that Arsene Wenger's side are unlikely to be serious title contenders this season.
"While I respect the opinions of Henry and Ljungberg, I believe this team can fight for the title," the former Barcelona trainee told the News of the World.
"What I say is not madness. We got to the Champions League final in 2005, often playing without players like Henry, Ljungberg and Ashley Cole.
"I have matured very much over the last two years and I am prepared to be the leader of the team.
"Maybe then people won't ask me any more about becoming the next Patrick Vieira!"
Fabregas added: "I would love to captain Arsenal. It is a matter of enormous pride to me because the fans are always with me and that support is very valuable.
"I know how the fans suffer when we lose."