The 41-year-old American was a huge underdog against rising prospect Price, but turned back the clock to stop the fight in round two.
Now Thompson says he wants to fight Britain's other big heavyweight prospect Fury.
"I took care of David Price like I said I would," Thompson told BoxNation afterwards.
"Now I want that sissy Tyson Fury next. He's been talking a lot of noise and I want him next."
Fury is currently getting ready to make his American debut in April. He and Price are yet to meet in the ring despite a lot of trash talk, and it remains to be seen whether a fight against Thompson is on Fury's radar.