Finney injured his knee near the end of the morning session Wednesday, walking gingerly before leaving the field on a cart.
Beckman said the 6-foot-1, 205-pound sophomore was in good spirits at lunch and was upbeat before the day's second practice in the afternoon.
"We're going to be positive and find out what the results are from the doctors and we'll see what the condition is," Beckman said.
Finney enrolled as a junior college transfer in January and earned a starting spot with his play in spring drills.
"He's a guy who has worked his tail off this offseason," said sophomore linebacker Mason Monheim. "He earned a spot. We pray that it's not too bad. I talked to him a little bit. But at a time like this, there's nothing you can really say. You just hope that everything is going to be OK."
With Finney out at least for the short-term future, B.J. Bello is in line to take over the starting Star position, a safety/linebacker hybrid spot, for the time being.
A native of New Lenox, Ill., Bello redshirted last season in his first year on campus.
"He's young. He's a freshman, redshirt freshman, but again he's been here now, his body's matured, he runs well," Beckman said. "It's just as any freshman, he just has to mature."
Beckman mentioned starting safety Earnest Thomas could move to Star if necessary, as the junior spent time at the position in previous seasons. As with Finney's status, who exactly could be filling the role is still to be determined.
"You want to get your 11 best on the football field," Beckman said. "That's the key to anybody offensively and defensively, so whoever are those 11 best, that's who we'll get on the field."