Serena says she was 'nowhere near' Coco Gauff's level at 15

Serena Williams is chasing a 24th Grand Slam title in Melbourne. (Photo: AFP/David Gray)

The 38-year-old, one short of Australian Margaret Court's all-time record of 24 Grand Slam titles, fought off a stubborn Tamara Zidansek 6-2, 6-3.

Williams faces China's 27th seed Wang Qiang next and could meet her fellow American Gauff in the quarter-finals in Melbourne.

The former world number one and Gauff - touted as a possible long-term successor to Williams at the top of women's tennis - spent some of the off-season together.

Williams, sporting a pair of koalas painted on her nails in light of the devastation of Australia's deadly bushfires, was mightily impressed by what she saw in "fighter" Gauff.

"She's just impressive all-round, from her personality to the way she plays," said Williams, the top-earning female athlete in the world.

"I think it's just all super-impressive.

"I was nowhere near her level at 15 either on the court or off the court, not even close.

"I know kids are growing up different nowadays, so I'm not sure. But I was nowhere near as smart and eloquent as she is.

"It's nice to see."

Gauff turfed Serena's older sister Venus out in the first round in Melbourne, having done the same at Wimbledon last year.

Venus turns 40 in June, but Serena said she will be the first to retire out of the two sisters.

"Venus will outplay me, for sure, she loves tennis a lot," said Serena, who is in the twilight of her career but has given no hint that she plans to quit any time soon.

"She works hard on it, just gets unlucky sometimes health-wise obviously."

'A LOT OF ERRORS'

Williams was never in serious trouble against the 70th-ranked Slovenian Zidansek in their second round match at Rod Laver Arena.

But the 22-year-old Zidansek put up resistance in the second set with Williams twice failing to break when 40-0 up on her stubborn opponent's serve.

Eighth-seeded Williams described herself as "frustrated" by her failure to bury her opponent and she half-heartedly saluted the crowd at the end.

"I was making a lot of errors. Probably the most errors I've made since the start of the year," said Williams, whose last Grand Slam triumph arrived at the Australian Open in 2017.

Williams, who has won the Australian Open seven times, thrashed third-round opponent Wang 6-1, 6-0 when they met in the US Open quarter-finals last year.

Williams dropped just three games in her opening win over Russian teenager Anastasia Potapova on Monday in Melbourne.