"I've never faced her, but I've kind of become a fan with everyone rooting and cheering so hard", Williams said.
But since then, Osaka split with with her coach Sascha Bajin and has been unable to refind the form that saw her storm her way to a world number one ranking, suffering early eliminations in multiple tournaments including a first round exit at the 2019 Wimbledon Championships , before coming unstuck against Williams in straight sets 6-3, 6-4 this week, in Toronto.
Williams spoke after her match but before she knew who she would face in the quarter-finals, saying either Osaka, who could return to the world number one ranking next week or Swiatek would be worthy foes.
But with the year's fourth grand slam just around the corner, Williams showed she still had the game to claim a 24th major title by defeating Osaka 6-3 6-4.
There was no such drama in Toronto, where Williams broke Osaka for a 5-3 lead in the first and closed out the opening set with a service victor.
"It was just a better match for me today", Serena acknowledged in her on-court interview.
Osaka referred to Williams as her tennis mum in the build-up to the match.
"I knew her game a little bit more, so that's a little easier", Williams said post-match, according to The Guardian . She won in Indian Wells in March for her first WTA Tour title. "We haven't played since NY, which was a really good match for her".
"I just think that I gave her too many second serve looks, and she just did what she does".
In a rematch of last year's controversial US Open final won by Osaka, eighth-seeded Williams was firing on all cylinders against the second-seeded Japanese star. "So this is, like, such a big learning experience for me", Osaka added.
"I honestly don't really think there was ups and downs", Osaka said.
The Czech Marie Bouzkova, 91st World and qualifying, will be his opponent in Saturday's half: it has benefited from the abandonment after a set of the Romanian, ex-N.1 world, Simona Halep, embarrassed to a tendon d 'Achilles.
Pliskova eliminated Estonia's Anett Kontaveit 6-3, 7-5 to set up a last-eight clash with rising Canadian star Bianca Andreescu, who outlasted fifth-seeded Dutchwoman Kiki Bertens 6-1, 6-7 (7/9), 6-4. "Literally go home. My home is like two minutes from here".
Williams said she was looking forward to taking on Andreescu, whose run to the final has electrified Toronto crowds. My shoulder's good. I'm in the finals of the Rogers Cup.
"It was an up-and-down match, but a positive match for me", Nadal said.