Moffitt has remained without a ride since winning the championship last November at Homestead, Fla.
In his NASCAR career, Sauter, 40, has 23 wins and seven poles in 244 Truck starts. He has also won three races in the NASCAR Xfinity Series.
In an interview Wednesday afternoon with SiriusXM NASCAR Radio host Dave Moody, Sauter said he was only informed of the team's decision earlier in the day.
"GMS has been a great place, we accomplished a lot of things. If they don't need me, you don't need to be there," Sauter said. "Like my dad always said, 'If you're hand ain't broke, you'll never go hungry. So, I'll figure out something to do."
Asked what was next for him, Sauter said, "I don't have a clue. Rides are pretty scarce, rides that you want to drive. We'll just have to see what shakes out. It's one of them deals where I'm not going to drive junk.
"If an opportunity doesn't present itself, I don't have to do it."