Naomi Osaka will be confirmed as the world No.1 next Monday following the conclusion of the quarter-final matches at the WTA Premier 5 event on Toronto.

It's definitely not where I want to be, but I'm getting there Serena Williams

Osaka and Karolina Pliskova were the two who were angling to take over from Ashleigh Barty who lost early in the week but the Czech had to at least reach the final to have any chance of regaining the place she last held in 2017. And only then if Osaka fell either before the final or was beaten by the Czech in the title round.

As it turned out, both were beaten in the last eight leaving Osaka ahead on points.

Osaka lost to Serena Williams in the rematch of their controversial US Open final when the American suffered a major meltdown.

On this occasion Williams dominated as she fired 12 aces with some strong service games to beat the young Japanese star for the first time in three meetings, 6-3 6-4.

She never looked threatened and even a brush with the net cord as she raced forward trying to run down a drop shot, didn’t faze her.

“It hurt, but it wasn’t the end of the world,” Williams said later.

The American’s lone wobble came in the final game. After a pair of aces gave her a triple match point, Williams offered up a double fault and two backhands into the net before she closed it out with an ace on her fourth match point.

“We haven’t played since New York, which was a really good match for her,” said Williams, adding that she feels her own game is building as she hoped in a positive way for the US Open later this month.

“I’m getting there,” said Williams, who hasn’t dropped a set all week as she pursues a fourth Toronto title. “It’s definitely not where I want to be, but I’m getting there.”

Reflecting on her own performance, Osaka believed she played too defensively but wasn’t really allowed to get a foothold on the match.

“But I think there were chances where she hit shorter balls, but I wasn’t expecting her to hit the shorter balls, so I didn’t move up on time,” she said.

In the semi-finals Williams will face Czech qualifier Marie Bouzkova, who advanced when Wimbledon champion Simona Halep retired with Achilles tendon trouble after dropping their first set 6-4.

“I’ve always wanted to play Serena,” said the 21-year-old Bouzkova, ranked 91, on dismissing her third grand slam champion of the week, Sloane Stephens, Jelena Otapenko and now Halep. “It’s always my dream to play against her.”

The Romanian admitted she had been bothered by her Achilles tendon from the start of the tournament.

“And today I felt it more, so that’s why I decided to retire,” said Halep in what was no doubt a cautionary move ahead of the US Open.

Meanwhile it was Canadian teen Bianca Andreescu who upset the apple cart for Pliskova when she pulled off a 6-0 2-6 6-4 win after one hour and 49-minutes and end her top spot aspirations.

Andreescu advanced to a semi-final clash with American Sofia Kenin, who defeated Ukraine sixth seed Elina Svitolina 7-6(2) 6-4.