Rose made his feelings known before Friday night's preseason contest against the Pacers.
While being respectful regarding Indiana's recent success, Rose acknowledged that he believed any rivalry with the Pacers is a thing of the past.
"People say that it's a rivalry, but I don't really see it," Rose said before scoring 32 points in the team's 103-98 win against the Pacers. "I say the team that is more like a rivalry is when Darren Collison was on the team. That one was more like a rivalry, but this team is a great team. They've already proven themselves last year by making it to the Eastern Conference finals.
"If anything, by probably in a year or two, it could become a rival. But right now, people say it's a rival. ... I just don't see it right now."
Rose and the Bulls defeated the Pacers in the first round of the playoffs in 2011.
Asked what made the rivalry with the Collison-led Pacers different, Rose responded this way:
"I think it was more like that rivalry feeling where we knew, we thought that they were going to have that same team for a long period of time," Rose said. "Then they end up going different ways, picking up different guys, and I think this team, I think in the next year or two, if both teams have the same teams, then that's when it would become a rivalry."
Asked specifically if he felt the Heat were the Bulls' biggest rival, Rose acknowledged that to be the case.
"If you want say [that], yeah," he said. "For sure, Miami."
For their part, the Pacers have repeatedly talked about the rivalry they feel they have developed with the Bulls over the years.
"I think Chicago will always be a rival," Pacers forward Danny Granger said recently. "When you go to the United Center, it's crazy. They have a big home-court advantage there. They have a huge following, not only locally in Chicago but nationally as well, and I think they'll always be a rival to us. We're really close, so a lot of times there's a lot of Bulls fans here and vice versa. I think as long as we're in the division, we're going to be rivals."
Bulls coach Tom Thibodeau was complimentary of Indiana when asked about a potential rivalry with the Pacers.
"We're all battling for the same thing," he said. "They're deep, they're talented, so we know how good they are. They have size, quickness, toughness, they play together, they play smart, they're well-coached. They're one of the elite teams in the East for sure."