"She's a force to be reckoned with": Serena Williams looks forward to playing Ash Barty.

— With AAP.

On Saturday, World No. 1 Ashleigh Barty, 23, casually cruised through to the fourth round of Wimbledon after a 6-1 6-1 rout against unseeded British wildcard Harriet Dart.

Serena Williams also made it through to the last 16, ensuring the two grand-slam champions are on track to meet in the Wimbledon quarter-final.

The likely last-eight showdown against Williams is tipped to be Barty’s sternest test yet in her Wimbledon campaign.

Bidding for a record-equalling 24th major, and eighth Wimbledon crown, Williams has admitted she’s been keeping a close eye on the top seed’s progress.

Williams and Barty first met when the Australian was a teenager at her home slam in 2014.

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“I’ve always from the day I played her in Australia had a tremendous amount of respect for her game,” Williams said.

“I just thought she’s just a beautiful player. She has great technique. I love that.

“I’m really a technical player. I like when people have a beautiful game and they do the right techniques. It’s so right up my alley.

“I’ve seen her play a lot recently, too. Like I always say, she’s just someone in the locker room that you just always root for.

“But in general I have been watching her game because I know that she’s a force to be reckoned with. So I’ve been watching a lot.”

With Barty having not dropped a set in her past 10 matches, a duel with Williams appears inevitable.

When asked about the potential quarter-final match against the former World No. 1, Barty replied: “I will give the athlete’s answer and say: I’m just going to worry about Alison first.”

Williams' praise for Ash Barty comes after the 37-year-old was criticised for not knowing Ash Barty was the World No. 1 at the start of Wimbledon.

Williams was informed of Barty's top seeded position during a pre-Wimbledon press conference. She did however say she was happy for the Queenslander, telling the media, "Wow, that's great!"

"Obviously I'm happy for her. Yeah, it's good. It's good for her."

Barty will next play unseeded American Riske in the round of 16 on Monday, seeing a seed-free path to at least the last eight for the World No. 1.

Dual Wimbledon winner Petra Kvitova continues to loom as a potential semi-final threat to Barty and Williams after marching on with a 6-3 6-2 dispatch of Poland's Magda Linette.

Like Barty, sixth-seeded Kvitova, champion in 2011 and 2014, has yet to drop a set.

For more on this topic:

• "Everyone has their own journey": Ash Barty's take on Kyrgios and Tomic shows why she's world No. 1.
• "Still the same person." The photo that tells you what you need to know about Ash Barty.
• Ash Barty: The face of Australian sport we can all be proud of.