Naomi Osaka and Serena Williams to meet in Rogers Cup quarters

Naomi Osaka and Serena Williams are set to meet in the quarter-finals of the Rogers Cup for their first meeting since last year's dramatic US Open final.

On Thursday, Williams knocked out qualifier Ekaterina Alexandrov 7-5 6-4 in the round of 16 with Osaka prevailing over 18-year-old Iga Swiatek 7-6 (7-4) 6-4.

Osaka holds a 2-0 record over Williams and the most recent of those victories was the highly-charged and memorable affair at Flushing Meadows.

The 6-2 6-4 US Open final victory saw Osaka win her first career Grand Slam but it was a night in which Serena's conduct on court, and her outburst towards the chair umpire Carlos Ramos, moved the spotlight away from Osaka's work.

Since, Williams has spoken about the impact that the evening had on her too, and shared that she wrote an apology to her younger opponent. As a result, the dynamic between the two on Friday will be fascinating.

"I'm just really excited," Osaka said about the quarter-final clash which is third on Centre Court in Toronto.

"I grew up watching her, so whenever I get the opportunity to play her, it's something that I feel is a once-in-a-lifetime opportunity."

It feels more like I'm showcasing my skills to her, like, 'Look what I can do.' You know what I mean? So I go into the matches with that mentality, and I'm just super grateful to get the chance to play her.

Williams, a three-time winner of the Rogers Cup, has a formidable record at the competition. In eight of her nine career appearances, she has only failed to reach the semi-finals on one occasion and has a 32-4 win-loss record.

This week in Toronto, the 23-time Grand Slam champion has been down a break in all four of the sets that she has played in but has shown the fortitude to come back in every one.

In front of an enraptured crowd, Bianca Andreescu played out her third three-set match in a row to oust the fifth seed Kiki Bertens 6-1 6-7 (7-5) 6-4.

Andreescu's victory over Bertens, the world No 5, pushed the Canadian out to five wins without defeat against top 10 opponents this year.

Despite the fact that the 19-year-old's competitive tennis has been limited leading into this tournament, hampered by a shoulder injury, she believes that that has actually helped her.

"Being off for that long and coming into the Rogers Cup and getting into the quarter-finals means so much to me," said Andreescu. "This time off actually really helped me. I figured a lot of things out and it's showing on the court."

The teenager's opponent in the last eight, and the player looking to stop her becoming the first Canadian woman to reach the semi-finals, is the world No 3 Karolina Pliskova who surpassed Anett Kontaveit 6-2 7-5 on Thursday.

Alongside Osaka, Pliskova is in the race to become the new world No 1 on Monday after Ashleigh Barty's early tournament exit and neither will want to slip-up at this stage of the tournament.

Elsewhere on Thursday, Elina Svitolina navigated her way past a plethora of challenges in order to book her quarter-final spot.

During her 6-2 6-4 victory over Belinda Bencic, the sixth seed rolled her ankle early on, handled the disruption of a 90-minute rain delay and kept her cool despite letting four match points go astray.

After handling all of that, a meeting with the conqueror of Barty awaits and the clash with Sofia Kenin is one that Svitolina feels that she's prepared for.

"I played against [Kenin] in Indian Wells and didn't know much about her game," said the Ukrainian.

"Now we've seen a lot of matches of hers because she's been winning a lot and playing some great tennis.

"So it's going to be another tough battle, and I will try to be physically ready and mentally just be there and try to earn my chances, and just play my game."

Simona Halep's 6-2 6-1 victory over Svetlana Kuznetsova took just 67 minutes and that would have been a welcome relief after her two-and-a-half hour marathon against Jennifer Brady in the previous round.

Halep has now won 13 of her last 14 Rogers Cup matches and will look to extend that record against Marie Bouzkova, who is now preparing to play in her first WTA quarter-final.

Bouzkova, the world No 91, also enjoyed a straightforward win on Thursday.

Her 6-2 6-2 triumph over Jelena Ostapenko continued the qualifier's excellent form as she capitalised on Ostapenko's 10 double faults and saved all four break points against her.