Coco Gauff says she was “not too nervous” to play in front of the great Rod Laver because she was already well on the way to reaching the Australian Open quarter-finals when he arrived.

Playing on the court named after the 11-time major champion, Gauff swept past Magdalena Frech in a 6-1 6-2 win.

“Luckily I was up a lot when I noticed he came in,” joked fourth seed Gauff.

Defending champion Aryna Sabalenka continued her own serene progress by beating Amanda Anisimova 6-3 6-2.

American teenager Gauff remains on course to meet Sabalenka in the Melbourne last four, which would give the Belarusian an opportunity to avenge her defeat in their US Open final.

Like Gauff, second seed Sabalenka has not dropped a set at the first Grand Slam tournament of the 2024 season.

Gauff, who has not faced another seed, will play Ukraine’s Marta Kostyuk next, while Sabalenka faces either teenager Mirra Andreeva or Czech ninth seed Barbora Krejcikova.

Seeded players have been falling quickly in the women’s singles, with only four of the top 16 left after the first week and just seven remaining in total.

Belarusian Victoria Azarenka, seeded 18th, is the only Grand Slam champion in the top half of the draw after world number one Iga Swiatek’s shock third-round defeat on Saturday.

Gauff, 19, ensured she did not face the same fate with a clinical and composed performance against Frech, who was competing in the last 16 of a major for the first.

After beginning the year by winning a WTA title in Auckland, Gauff continued a perfect start to the season by sweeping past the 69th-ranked Pole for her ninth straight victory.

The American broke serve in the first game on and allowed Frech to win just 10 more points in a 26-minute set.

Two more breaks of serve followed in the second set as Gauff breezed through without facing a break point.

In her first Melbourne quarter-final, she will face Kostyuk after the world number 37 easily beat Russian qualifier Maria Timofeeva 6-2 6-1.

Looking for a second major title after fulfilling her long-heralded potential in New York, Gauff is the second favourite behind 25-year-old Sabalenka.

Sabalenka has been in similarly devastating form – dropping just six games in her opening three matches – and producing another dominant display against 22-year-old Anisimova.

“I’m super happy with the level and happy to get this win,” said Sabalenka.