The 23-year-old Rose tore the ACL on April 28 during the first game of the Bulls' Eastern Conference quarterfinals series against the Philadelphia 76ers. Without Rose, the Bulls became only the fifth No. 1 seed to lose to an eighth seed as the Sixers won in six games.
"Derrick is doing great," Cole said Tuesday at a news conference at Rush University Medical Center. "The surgery went extremely well. Really no surprises. It was pretty routine.
"We're at this point very optimistic. ... We think of recovery as the long process that's in stages. But the short answer is the time frame we believe an athlete of this caliber generally requires is about eight to 12 months. Sometimes shorter, sometimes longer.
"While he will be at hopefully a very high level at 12 months, it still may take slightly longer for him to be at his pre-injury level. That's not uncommon for athletes of this caliber."
That means Rose is likely to miss at least the first two-plus months of next season, or he could miss the entire season.
"That's clearly the range of what's possible," Cole said.
Bulls general manager Gar Forman said Rose was ready for rehabilitation.
"In the time frame I've spent with him, and I was with him over the weekend, his spirits seemed really good," Forman said. "In his mind, he's determined to attack this rehab and get back to the level that he was at.
"There was a period when he was down. But I think his spirits are good under the circumstances, and I think he's ready to aggressively attack this."
When Rose does come back, Cole said: "Statistically, he should be that player [he was before] and then some. That doesn't mean it's guaranteed."
But Rose won't be rushed back.
"We're not going to rush it," Cole said. "The most important thing is all of us feel comfortable based on specific parameters that he's ready to go at each stage as we advance him. If he's not ready, we'll delay. If he's ready, we'll move him to the next stage.
"People do get back in six months after ACL reconstruction, but it's not common in a professional sport such as this with an athlete of this caliber, mainly because the downside of not being fully prepared is a worst-case scenario. We're trying to zero out the risk."
One important aspect of recovery, at least from a basketball perspective, is Rose learns to trust his knee again.
"If you look at reasons why athletes do or do not get back to their pre-injury level of play, there's no question that the psychological component is part of it," Cole said. "And because we know that, that's something we focus on.
"If you look at a typical progression, he'll be doing basketball-specific activities very early on. And that's just a great feedback move just to say, 'Hey, I can do this.' And then you do sort of non-contact, basketball-friendly activities against other people to start getting a sense of, 'Hey, I can do this, I can trust my knee.' And it's this progression of low contact, high levels of contact in competition, pre-playing a real game that they get the feedback and say, 'Hey, I can really do this.' ... He will learn to be able to trust his knee."
As far as the Bulls next season, Forman knows it's not going to be easy without Rose.
"Obviously short term we're going to take a hit," Forman said. "Our thinking in general long-term won't change at all. But short term obviously you don't replace Derrick, and what he brings to the team and the production he's got.
"But we're going to have to fill that spot, scrape it together in the meantime to fit in with our other guys."