Recent reports had suggested that the two could meet in the ring later this year.
"I've got no interest in fighting David Price. It's dead in the water. What's the point in fighting someone who was knocked out in two rounds? If I don't do the same to him then people will say I couldn't even do as good a job as a 41-year-old," he is quoted as saying by the Manchester Evening News.
"I had the opportunity to make big money out of fighting David Price. I was hoping to get him after Tony Thompson. Now a super fight in the summer has been messed up but maybe I'll get a big fight in America with Thompson.
"I was hoping Price would win. I didn't want him to lose because it is taking bread out of my mouth."
Fury is due to take on Steve Cunningham in New York in April.