Serena Williams says her motivation to win major trophies remains as high as ever in motherhood after reaching the US Open quarter-finals.

Williams, whose daughter Olympia turned one on Saturday, is aiming to win a record-equalling 24th Grand Slam title in New York.

The 36-year-old American former world number one is playing her seventh tournament since giving birth.

“That desire has not gone down at all,” she said.

“And I don’t think it was capable of going up, because if it was at a 10, I was at a 15 or a 20 – and I’m still there.”

Williams, seeded 17th, has been in fine form at Flushing Meadows, dropping her first set of the tournament before recovering to win 6-0 4-6 6-3 against Estonia’s Kaia Kanepi on Sunday.

Winning the US Open for a seventh time would see her level Australian Margaret Court’s all-time record of 24 majors.

• Williams beats Kanepi to reach US Open last eight
• Defending champion Nadal through to fourth Grand Slam quarter-final this year

Williams returned to Slam competition at the French Open in May, only to withdraw before her last-16 match against Maria Sharapova of Russia because of injury.

She then reached the Wimbledon final in July but lost to Germany’s Angelique Kerber.

“My desire still remained at that incredibly high level to compete and to want to win,” Williams said.

“It would be wonderful to win a Grand Slam while having a daughter, but it’s a lot of work.

“It takes a lot of work to win those tournaments. I’m only in my third one back. I’m going to continue to grind and see what happens.”

Meanwhile, Williams says she hopes to have more children in the future – but maybe not until after she finishes playing.

“Right now is not the time,” she said. “I’m thinking about playing tennis and enjoying this time with Olympia.

“I’ll have plenty of time in the future.”

‘It was a Serena scream’

Williams cruised to the first set in 18 minutes against Kanepi, only to see the world number 44 fight back to level in the second.

The Estonian missed two break points in the first game of the third set, allowing Williams to fight back and hold serve with a backhand winner, which brought out a loud yell of “come on” from her.

“It was a Serena scream,” Williams said with a smile. “I don’t try to do it. It just comes out.

“Winning a big game and a very important game and a really tight game, I think it was just a relief.”