Osaka saved two match points in a thrilling 4-6 6-4 7-5 win over 2020 runner-up Garbine Muguruza on Sunday.

The three-time grand slam winner will be hoping for an easier ride when she takes on world No.71 Hsieh Su-Wei of Taiwan.

Williams is up against world No.2 Simona Halep in Tuesday's other women's quarter-final.

Halep trails 9-2 in their head-to-head battles, but she thumped Williams 6-2 6-2 at the 2019 Wimbledon final in the most recent meeting between the pair.

The blockbuster rematch is sure to attract plenty of attention, especially with Williams still chasing Margaret Court's record of 24 grand slam titles.

Halep has the fondest of memories from that Wimbledon win over Williams.

"The game, I think it was one of the best in my life," Halep said.

"The best day actually of my life. I felt very confident back then. I felt every ball.

"But I'm not different mentally from that day. I just think that two matches in a row cannot be the same. I'm ready for a long match."

World No.1 Novak Djokovic will be aiming to continue his march towards a record ninth Australian Open crown when he takes on Germany's world No.7 Alexander Zverev on Tuesday.

Zverev won two of the first three meetings between the pair but Djokovic has since reeled off four straight wins against the German, including a come-from-behind victory at the recent ATP Cup.

Bulgaria's world No.21 Grigor Dimitrov will face surprise packet Aslan Karatsev in Tuesday's other men's quarter-final.

Russian qualifier Karatsev is ranked 114th in the world and is competing in his maiden grand slam.

Win or lose, the 27-year-old will receive the biggest pay day of his career.

Karatsev says even he's been impressed by his unexpected charge into the quarter-finals, and he looms as a fairytale story of the tournament.

Australian Associated Press