One of the most dominant athletes in any sport in a career spanning 22 years, Slater is likely to announce his retirement from full-time competition at the end of the event.
Parkinson has emerged as the major obstacle to a dream farewell for American Slater in enormous waves at the Billabong Pipe Masters.
Neck-and-neck in the rankings, Parkinson reached the quarter-finals on Sunday while Slater had yet to surf in round four when the event was called off for the day.
"It's turning into a bit of a foot race between Joel and I but we're not going to come up against each other until the final, if we get there," said Slater. "We're both just trying to put it out of our heads as much as possible.
"If you're thinking about it out in the water, you're taking your eye off the ball at Pipe. There's a lot to think about because it's such a challenging wave.
"You have to be clear minded and be making good decisions and that means concentrating on what's in front of you."
Slater and Parkinson were left as the only world title contenders following the shock elimination of Australia's Mick Fanning in round three by veteran American Shane Dorian.
Fanning was thrown onto the reef by a mountainous wave and required seven stitches to his left foot.
"Shane has been a hero of mine ever since I started surfing," Fanning said. "It was an honor to be in the water with him."
Parkinson and Fanning have been close friends for two decades, growing up together on the Gold Coast of Australia.
Battered, bruised and bloodied after a brutal heat in surfing's gladiator's pit, Fanning said he would stay in Hawaii to support his countryman.
Fanning had left Parkinson devastated by beating him to the world crown in 2009 but his countryman was the first person to greet him at the water's edge.
Parkinson lifted Fanning onto his shoulders and helped carry him through the 10,000-strong crowd in a selfless act at the most sorrowful moment of his 12 years as a professional.
"I remember that so well - if Joel wins it, I tell you, I'll be doing the same for him," Fanning said.
"I'm the first one there. For him to do that was crazy, it was so big of him. It shows what kind of a bloke Joel is.
"Now I'm out of it, there's nothing I'd rather see than Joel being world champion. He deserves it. He's just an insane surfer.
"I've got stitches in my foot and I'm limping round like an old man but if Joel gets it done, I'll be right there for him because he did the same for me."
Hawaii's Sebastian Zietz was a standout performer on Sunday, defeating Pipeline specialist John John Florence to claim the VANS Triple Crown, which tallies points from the prestigious events at Haleiwa, Sunset Beach and Pipeline through the winter.
(Editing by Peter Rutherford)