The Italian, whose number 25 shirt was retired by Chelsea after he stopped playing, took charge of the south east club in July some two years after his first management job ended with his dismissal from West Ham United.
In an interview with French weekly France Football on Tuesday, Zola said he wanted to become good enough to coach top clubs like Chelsea but was not yet the finished article.
"I have been dreaming of becoming a good manager. One who can lead a team like Chelsea," Zola said.
"I work really hard for it. I do not know if I will. I think I have the abilities but I do not think I am good enough yet.
"It is only my second coaching experience in a club after West Ham. I still have a lot to do," Zola added, saying the club's plans have matched his own ambitions.
"I am really pleased by the [owner's] plans. I know how serious the Pozzo family are. This is the best place I could have found to develop as a coach," the former Italy Under-21 assistant boss said.
