But the organization has not yet publicly narrowed down the list, and for good reason.
"You know what? Most of those guys are still playing," Harrison said. "As a matter of fact, they're all still playing. Somebody could get hurt, that sort of thing. My worst nightmare would be zeroing in on a guy and having him get hurt. Or something weird happens.
"... At this point, the horses are pretty well in the barn. We'll have guys at all the regional tournaments. We're seeing all these guys. We want to make sure that Matusz doesn't walk off the mound with a bad elbow, or Buster doesn't get hurt, whatever it might be -- [we're] just doing our due diligence. As far as what they do, those guys are our considerations, because they're all good players."
A year ago, Vanderbilt's David Price was the clear No. 1 pick in every camp. But no one player has managed to emerge from the group this year, which came as no surprise to Harrison.
"That's the way I saw it [back in the spring]," Harrison said, "and that's the way we still see it. Last year, we had a pretty good idea who we were taking in the fall. It was just a matter of something weird not happening to [Price]. But this group, this year, I can make a case for every one of those five guys."
While none of the five players mentioned have separated themselves from the group, Harrison likes the group.
"I would tell you all five of these guys, I've spent time with all five of them," Harrison said, "and our staff has spent time with them. [They're] all top-notch kids, they really are. You'd be proud to have any of them."
Harrison said he didn't know if they could sign one of the players before the Draft, which might be a consideration in who they select.
"Right now, we're just planning on taking the best ballplayer, and we'll get him signed," Harrison said.