The Spokesman-Review reported that Thompson's case stems from the purchase of an over-the-counter supplement that was not a steroid.
Thompson was named to the All-Pac-12 second team in 2017 and was honorable mention last season. He had six career interceptions and 190 tackles for the Cougars.
"I want to take a moment to thank my friends, family, Washington State teammates, coaches, staff and most of all Cougar fans and inform them that I will not be returning to Washington State for this upcoming season," Thompson wrote on Twitter on Saturday. "I am extremely grateful for the opportunity the coaches provided me at Washington State and wish my teammates nothing but the best for this upcoming season. I will always be a cougar and so appreciative of the tremendous fan support we always enjoyed! It is now time for me to take the next step in my football life and I embrace and look forward to the challenges ahead of me. Thank you and Go Cougs forever!"
The supplemental draft, which is open to players who did not declare for the draft in April, is set to take place during the second week of July.