"Probably five," O'Neal said Thursday on TNT's "Inside Stuff." "I'm going to go with five or six."
Bryant and O'Neal had a fractured relationship but the former Laker said that wasn't the reason why he left the team.
"We didn't have a bad relationship, because we won three out of four championships," O'Neal said. "That's not a bad relationship at all."
"It was a money situation, I was getting older," he continued. "They wanted me to take less money. I wasn't going to do that, so they traded me to Miami."
After joining the team together in 1996, the Lakers won titles in 2000, 2001 and 2002. The team was defeated by the Detroit Pistons in the 2004 NBA Finals.
"We won three out of four, it don't get no better than that," repeated O'Neal. "It doesn't matter how many fights we had, how many scuffles we had. It was the best one-two punch ever created."
O'Neal took some of the responsibility for his relationship with Bryant.
"A lot of that was created by me," O'Neal said. "I know he was a tough, ornery kid. I used to push his buttons. He used to push my buttons. It made us perform at a high level. He was trying to outdo me, I was trying to outdo him and it was hell for the opponents."
Bryant has since won two additional titles with the Lakers. O'Neal finished his career with four, winning with Dwyane Wade and the Heat in 2006.