So on some level, it's fitting their first pro game -- one that won't have fans, won't count in standings and will likely be long forgotten in a few days -- will pit them against one another. Rose's Chicago Bulls face Beasley's Miami Heat on Monday, one of three games that will open the Orlando summer league's weeklong schedule.
For a meaningless matchup, there's an abundance of big-game hype.
And it almost seems like neither 19-year-old can truly understand why.
"I didn't even know we're playing Miami first," Rose said. "I'm not going to be checking him."
"If you want to make it a Mike Beasley and Derrick Rose show, go ahead," Beasley said. "But that's not how it's going to be."
Rose, the No. 1 selection in last month's draft who led Memphis to the NCAA title game, will be running the Bulls offense from the point guard spot. Beasley, the No. 2 choice by Miami after averaging better than 26 points and 12 rebounds in his lone season at Kansas State, will be posting up against the likes of Chicago big men Joakim Noah and Tyrus Thomas.
They won't guard one other and, outside of a pregame handshake or some idle chitchat during stoppages of play, probably won't interact much at all.
"I don't feel that every time you mention Derrick Rose's name, you've got to mention mine, or vice versa," Beasley said. "If people want to, they can. But I've got my career to look after. He's got his."
Teams will play five games in five days at the summer league, which also features Indiana, Oklahoma City, New Jersey and Orlando, with each squad playing all the others once. Most of the players are either rookies or second-year pros, most of them simply fighting for jobs in the NBA this coming season.
Beasley and Rose don't have to worry on that front.
That doesn't mean they enter this week with no concerns, however.
Rose has spent the past few days battling tendinitis in his right knee, something that he dealt with at times during his lone season at Memphis. And Beasley missed some summer-league practices with the Heat after suffering a slightly cracked sternum during a defensive drill 45 minutes into the team's first workout.
He will play in Orlando wearing a specially built pad to protect his breastbone, a device that Heat trainer Jay Sabol cobbled together.
"I'm going to play until my chest caves in," Beasley said. "I feel it in everything I do, but I'm not going to be soft about it. I'm not going to baby it."
The Heat have been assured that there is no additional risk in putting Beasley on the floor this week. He'll feel some pain, and will certainly be tested by opponents who may try to put an extra shoulder or elbow into his chest because they know he's ailing, but Miami's medical staff believes there's no chance of the injury turning into a long-term area of concern.
"He's cleared. He's ready to go and he's eager," Heat coach Erik Spoelstra said. "We've consulted with the doctors and they say it's fine. So, he feels fine. We have a lot of protection out there. ... We feel very comfortable about it."
Spoelstra won't be coaching Miami's summer-league entry; that job goes to longtime Heat assistant Keith Askins.
Instead, Spoelstra's job will be evaluating the entire Heat roster from the bleachers, and he doesn't sound like someone who'll demand immediate dominance from Beasley, either.
"I think it's more important that he gets an understanding of what our system is," Spoelstra said. "He's going to be playing against NBA guys soon enough and that's a great opportunity on Monday to play against Chicago's front line. And they have experience. It'll be a great challenge for him. But this opportunity for us is to help him learn our system, get accustomed to how we do things."
Beasley said he just wants to play, whether it's against Rose or not.
"I'm pretty anxious. I haven't been real competitive since the [NCAA] tournament," Beasley said. "So it's going to be fun, man, to beat up on some other guys for a change."