Yes
Why- he has not yet fielded a team that will make or go deep into the post-season. He has brought in some great players, and some players have grown and developed, but great players don't always = great teams.
This is his third year, and it doesn't look like UT has a very good shot at making the post-season again. Sometimes coaches aren't great fits at certain schools, or the timing is off (the list of excuses go on and on) but whatever case, it's just not working out.
I would start the search now, make nothing official, let him finish the season, and give him the pink slip as soon as the season comes to a close. There are a lot of people pushing for Pat Murphy, but instead of trying to hire him as the next coach, I would enlist his help for finding the next coach.