"Because I'm on a mission, and until I accomplish this mission, I'll be right here," Zambrano told ESPNChicago.com on Friday.
The mission Zambrano speaks of has kept Cubs owners and managers up at night for 102 years.
"Of course, to win the World Series here," Zambrano said. "It's not just me, I have confidence in my teammates that we can do it."
Zambrano is 7-0 with a 1.27 ERA in 10 starts since returning to the Cubs' starting rotation on Aug. 9. He had three relief appearances prior to that after being activated from the restricted list on July 30. Zambrano was placed on the restricted list following a dugout altercation with former teammate Derrek Lee on June 25.
Zambrano will have a chance to accomplish his goal over the next two seasons as his contract runs out after 2012. The team owes him $36 million.
As far as his immediate goal, Zambrano said it's a matter of conditioning.
"Be healthy, and stay in shape," he said. "I will work hard to be in the best shape I've ever even been in.
"And I look forward to leading this team. I have discipline for what I eat and how I work. Going to Arizona in the summer while I was on the restricted list was a good thing for me. It's one of the best places to get in shape, and that helped me a lot."
Bruce Levine covers baseball for ESPNChicago.com and ESPN 1000.