The 6ft 8in Liverpool heavyweight has his long-term sights set on a clash with either WBC champion Vitali or his brother Wladimir, who holds the WBA, IBF and WBO belts.
First however, the unbeaten Price faces a step up in class against American veteran Thompson, who has lost twice to Wladimir in the past.
The British champion knows he can make a statement to the world by beating Thompson even more impressively than Klitschko, who needed 11 rounds to stop the Washington man in 2008 and six in July last year.
“It’s the biggest fight of my career,” Price told Press Association Sport.
“The ideal scenario is that I do a real number on him – better than Wladimir Klitschko did.
“I’m not Wladimir Klitschko, I’m David Price, so at the end of the day I need to do what’s best for me. That means keeping a professional, focused mentality during the fight and if an opportunity comes to finish the fight early then I’m definitely going to go for it.
“Beating him in style is the ideal scenario but I’ll take any kind of win.”
Price (15-0, 13 KOs) revealed tomorrow’s bout at Liverpool’s Echo Arena will not be his first time in a ring with Thompson (36-3, 24KOs).
“When we went with England to America in 2007 for the World Championships in Chicago we stayed in Philadelphia for 10 days or so and Tony Thompson was in the same gym as us,” he said.
“I think I sparred one round with him, which he won’t remember as it wasn’t really memorable. It was like a lifetime ago, when I was an amateur. That’s the only time I’ve come across him. We had a little chat and he gave me a bit of advice.
“It’s gone full circle now and here we are, about to fight each other.”
Thompson, 41, knows this is a make-or-break fight for him too.
“Price’s team have picked me because they think I’m just a name to look good on his record,” he said.
“They think I’m past my prime and they are making a mistake. This fight will tell us something and I’ll be honest, if he blasts me out then I know it’s over for me. But I don’t believe it’s my time yet.”