NEW YORK >> The next woman who must deal with the daunting task of playing Serena Williams at the U.S. Open, Ajla Tomljanovic, considers herself an admirer of the 23-time Grand Slam champion.

“I’ve been a Serena fan,” Tomljanovic said, “since I was a kid.”

Tomljanovic, an Australian who is 29, will face Williams, who turns 41 next month, for the first time tonight — in front of what is sure to be another exuberant and partisan full house — in the third round at Arthur Ashe Stadium.

“She kind of has that aura, like Roger (Federer), Rafa (Nadal), and deservedly so,” Tomljanovic said. “I always get happy when she says ‘Hi’ to me.”

Tomljanovic recalled watching on TV as Williams won major trophies. Also tuning in over the years — but never across the net from Williams in a match until this U.S. Open — was the player Williams beat in the second round on Wednesday, No. 2 seed Anett Kontaveit, who’s 26. Same for the player Williams beat in the first round on Monday, Danka Kovinic, who’s 27.

This is not why Williams is winning these contests in what is expected to be the last tournament of her career, but it sure can’t hurt.

Must not be easy to try to defeat someone whose success is oh-so-familiar, someone you looked up to before you turned pro yourself, someone you admire to this day.

“Oh, it factors in a lot. When I was young, I knew I had to beat members of a certain generation to move up. And Serena’s always been the one to beat,” said Billie Jean King, the Hall of Famer who won 12 Grand Slam singles titles in the 1960s and 1970s, plus another 27 in women’s doubles and mixed doubles.

“It can work in your favor if you thrive on playing the best player ever and you know it’ll help your career if you win,” King said in a telephone interview Thursday. “But the other side of the coin is, ‘Oh, no! I have to play her?’ And with the crowd, the history, you really have to try to embrace the situation and the occasion.”

That certainly is not easy.

Especially when Williams is playing as well as she did against Kontaveit, particularly in the moments that mattered the most in the 7-6 (4), 2-6, 6-2 victory — the first-set tiebreaker and the third set.

“Well,” Williams said with a laugh, “I’m a pretty good player.”

Sure is.

And her opponents sure know it, of course.

Back when Williams and her older sister Venus — who lost in the first round of doubles together Thursday night — were swapping the No. 1 ranking the way other siblings might share clothing and meeting each other in nine all-in-the-family finals at Grand Slam tournaments, they often took the court with something of an advantage that went beyond their considerable talents.

Some other players were simply in awe.

So even though Williams plays less, and wins less, nowadays than she used to in her heyday — her 2022 record was 1-3 before this week — listen to what Kovinic had to say about learning she was drawn to face the American at Flushing Meadows: “I was happy. I won’t lie. I’m honored to play against her, never mind whether I win or lose. It’s a privilege to share the court with Serena.”

How did that go? Williams won 6-3, 6-3.

Here is what Kontaveit’s thoughts were when her matchup against Williams was assured: “I’m really excited. I was really rooting for her to (advance to the second round). I’ve never played against her. I mean, this is the last chance. Better late than never.”

Kovinic and the 46th-ranked Tomljanovic expressed similar sentiments.

Jessica Pegula, a 28-year-old American who is seeded No. 8 in New York and won Thursday to reach the third round, played Williams once, losing to her in the final of a tournament at Auckland, New Zealand, in January 2020.

“I knew it was a big moment. … I felt OK, but then once we started playing and you could kind of feel her power — and feel her hitting a winner, coming at you, serving — I think that’s when you’re like, ‘Oh, wow, I’m playing Serena,’” Pegula said. “I think we all kind of have those moments for the first time.”