Aryna Sabalenka has achieved one ambition already at the US Open, and now she has the chance to fulfil another dream.

Belarusian Sabalenka, the second seed, found out she will become world number one for the first time next week after Iga Swiatek’s defeat by Jelena Ostapenko on Sunday.

The 25-year-old then moved into the quarter-finals at Flushing Meadows after a 6-1 6-3 victory over Daria Kasatkina.

“I had no doubt that Iga was going to make it to the final. I was sad that she lost, but becoming number one means a lot to me,” said Sabalenka.

The final 8 are locked in on the women's side pic.twitter.com/m3Tkt7zpfU

— US Open Tennis (@usopen) September 5, 2023

“I’ve been pushing myself a lot this year to make this goal and I still can’t believe it, but I didn’t want to be distracted for tonight.”

Swiatek’s defeat also means there will be a new women’s champion this year, with Sabalenka the hot favourite.

She will face China’s Qinwen Zheng, who ended the hopes of last year’s runner-up Ons Jabeur, in the last eight.

Wimbledon champion Marketa Vondrousova moved a step closer to back-to-back grand slam titles by beating Peyton Stearns.

Marketa is moving on! pic.twitter.com/dsd9REqoc1

— US Open Tennis (@usopen) September 4, 2023

The 24-year-old Czech, seeded ninth here two months after becoming the first unseeded woman to win at SW19, fell a set behind to Stearns.

But the American youngster, whose powerful forehand accounted for Britain’s Katie Boulter in round three, won just five more games as Vondrousova triumphed 6-7 (3) 6-3 6-2.

“She was playing great from the beginning and I just tried to stay in the game,” said Vondrousova.

“She is a very dangerous player, she has a great future ahead of her and it was a very tough match.

“I’m very happy. I didn’t expect this, after Wimbledon there was a lot of pressure but I’m feeling good and we’ll see what happens next.”

What happens next is a meeting with Madison Keys, a former Flushing Meadows runner-up who sprung a mild surprise against fellow American Jessica Pegula, the third seed.

Keys, seeded 17, is emulating the form which swept her to the final in 2017 and sunk the highly-fancied Pegula 6-1 6-3.

The 28-year-old said: “It’s always tough having to play a friend but we’ve been doing it all our lives. On court it’s all business but then we go back to being friends.”