The right-hander, who was traded on Jan. 5 to the Marlins for Chris Volstad, is not scheduled to start against his former team. Zambrano's winless in two starts so far and has walked eight over 12 innings.
"I don't want to pitch against the Cubs -- not yet," he said.
Zambrano harbored hope that he would stay in Chicago, where he compiled a 125-81 record since 2001. He flew to Chicago from Venezuela to meet with president of baseball operations Theo Epstein in December to discuss that.
"I had hope," Zambrano said. "Obviously, like I always say and people know, this is a business. Sometimes they need somebody who fits better than me over there and the people in Miami need me here, and that's why they made the trade and I'm ready to do my job."
He made the decision to waive his no-trade clause and accept the deal after talking to his family, including his 11-year-old daughter.
"She said, 'Daddy, whatever you decide, I'm with you,'" Zambrano said. "It was a family decision, too, it was not only my decision. It was a family decision and my family felt it was time to move from Chicago."
Zambrano had a volatile career with the Cubs that included a no-hitter in September 2008 plus a few temper tantrums and time to undergo anger management therapy.
"I know I made a mistake in Chicago, I made a lot of mistakes, but I have a lot of good memories about the Cubs," Zambrano said. "I accept my mistakes. I'm responsible. I don't make excuses. I'm responsible for things that happened in Chicago, nobody else. It wasn't [former general manager] Jim Hendry, it wasn't the team, it was me, Carlos Zambrano.
"That's why I'm here. I wanted to play the whole time with the Cubs because that was the team that brought me up and the team that discovered me and gave me a chance and the opportunity. Things aren't like that."