In Tuesday's interview with the Gazzetta dello Sport, Materazzi disclosed that after he held his opponent's shirt, Zidane said: "If you want, I'll give you the jersey later."
"I responded that I preferred his sister, it's true," Materazzi said. "It wasn't something nice, true. But luckily there have been dozens of players who have confirmed that a lot worse things are said on the field."
Zidane was sent off after receiving a red card for the head-butt. Italy went on to win on penalty kicks.
Materazzi received a two-game ban for the July 9 incident and will miss Wednesday's rematch of the final, a 2008 European Championship qualifier. Zidane received a three-match suspension, but he retired after the World Cup.
Materazzi said that the Italian federation, in the middle of a match-fixing scandal, told him not to complain about the incident during a FIFA hearing.
"If accepting without raising my voice was the price to pay for having brought home the World Cup, I'm pretty happy to have paid it," Materazzi said.
Asked if the two could make peace, Materazzi said: "You sign a peace (agreement) after terrible wars, so why can't Zidane and I make peace?
"A peace among men, without a lot of publicity. The door to my house will always be open for that. And if Zidane wants, he knows where to find my address."