Butler had medical evaluations Thursday and will work out Friday for NFL teams.
"I am not necessarily looking at this week as a make or break opportunity," he said. "Fortunately, I have built a pretty good foundation. I am looking forward to what I can show this week to kind of put a cherry on top of a good career and move myself forward."
Butler averaged 44.2 yards per kick with a long of 62 this season.
"I want to show that consistency and coachability and how I can perform and get that ball to do exactly what I want on every single punt," Butler said. "I think that is something I have been able to do the past three years and something I am looking forward to doing in the NFL to show these coaches I have what it takes, and I'm the top player in the country this year."