Price, 29, was caught on the side of the head by a right hand from Thompson after a quiet first round, and Fury now sees ‘The Tiger’ as an ideal fight for Tyson once they have taken care of Cunningham in the US on April 20.
“I can’t say I thought much of the fight. Price fell like a deck chair as soon as he was hit with anything,” Fury told World Boxing News.
“Tyson will take Thompson after Cunningham and show Price how to deal with an old guy.
“Thompson is an old nobody. We would take him as a warm-up for Pulev later in the year and show the public how he should be dealt with.”
Fury, 24, was linked to a possible £1million showdown with Price for years. He has now seen that cheque wiped out by Thompson with one swift punch.
The only way Fury and Price could make any real money in a big UK clash is if either one held a world title.
It could now be over a year before the fight comes back into domestic reckoning.
Price would need to avoid another defeat in the interim.