Morse, a senior, has been Wisconsin's top punter for three years but has faced persistent competition from redshirt freshman DeBauche.
"We gave it through this week," Murphy said. "We're looking at film tonight and…we'll see where we're at at that time."
Morse, DeBauche and the Badgers' third punter, Paul Standring, have had their hang time, distance and accuracy charted each practice since formal workouts began.
"They've been up to speed on it and they know that this was going to be a big week," Murphy said. "It's who's punting the best right now. And we'll go from there."
Murphy would not tip his hand, but did say that the team may use both Morse and DeBauche.
"I think we're definitely looking to improve our pooch punting, our plus side of the field punting, and I think there is a role for both, if it presents itself," Murphy said.
Both DeBauche and Morse have improved from last season, Murphy said, making the competition even tighter.
"It's turned out to be a great battle. It's been neck and neck all the way," he said.
DeBauche made an impression from the first moment he arrived at Wisconsin last year, immediately improving the Badgers' comfort-level with the punting game, which was a sore spot the season before.
"I think Kenny's really talented," Murphy said. "He's got a big leg, fundamentally he's very sound, he's consistent, which Kenny's problem last year was he just was in that, like any freshmen, he was up and down at times and he showed rays of what he can be, but on a consistent daily basis he wasn't there. But this year he's really proven to be (consistent)."
Morse has amassed the sixth-most punting yards in school history and has a career 39.3 yards per punt average. He played six games and split time as the No. 1 punter as a true freshman, averaging 41.6 yards per punt. An injury kept him out of five games that year. He struggled as a sophomore, averaging just 37.4 yards per punt but rebounded last season to average 40.7.
"R.J.'s really improved. From operation time to hang time through to consistent distance has really improved. He's worked hard at it," Murphy said.