NEW YORK -- The question posed to Serena Williams was rather simple.
Is it fair to say Sloane Stephens has emerged as a rival heading into their fourth-round showdown Sunday at the U.S. Open?
Stephens is, after all, one of only three women to beat Williams this season. She's also one of only three women -- Williams, naturally, is another -- to reach the round of 16 at every Grand Slam tournament in 2013. And Stephens is climbing up the rankings, enough to be seeded 15th at Flushing Meadows behind No. 1 Williams.
Faced with that query in the wee hours of Saturday, after both women had won in the third round to set up their much-anticipated match, Williams exhaled.
"I don't know," she began. "I mean, definitely. I mean, anyone that's playing tennis and that's doing as well as her, you can definitely say that."
From the moment the draw came out at Flushing Meadows, there was one particular possible match in the fourth round that grabbed attention: defending U.S. Open champion Williams against the up-and-coming Stephens, the top two American women.
"It's something," Stephens said, "I think everyone is looking forward to."
Williams is 31 and owns 16 major titles. Stephens is 20 and already carrying the label of "Next Big Thing." The last time they played each other, in the Australian Open quarterfinals, Stephens surprisingly won, one of only four losses in 67 matches for Williams in 2013 (she was beaten by Victoria Azarenka twice, and Sabine Lisicki once).
And then there's this: Stephens found herself in a bit of a brouhaha this year over less-than-flattering comments she made to a reporter about Williams.
"That's all old news now, and we've moved on. We're fine, so I think that's all that matters," Stephens said Friday.
Asked about her relationship with Williams, Stephens replied: "Obviously, we're co-workers. We're Fed Cup teammates. But other than that, everything else is private."
When the "co-workers" portion of those comments was relayed to Williams, she said: "We're teammates. I mean, I've always really liked Sloane. I have a lot of respect for Sloane. I think she's a great girl. I think she's great for tennis, as well."
Before their enticing rematch, Williams will be on court Saturday, teaming with her older sister in doubles. Also on Saturday's schedule are singles matches for past U.S. Open champions Roger Federer and Rafael Nadal, along with the top American man remaining, No. 13 John Isner.
Meanwhile, the buzz for Williams-Stephens will keep building.
"As I always say," Stephens said, "I think it will be epic."
She spoke those words hours before Williams even had advanced out of the third round by beating 78th-ranked Yaroslava Shvedova of Kazakhstan 6-3, 6-1 in a match that wrapped up at 1:05 a.m. Saturday. They weren't able to get started until nearly midnight -- Williams said she killed time by watching "I Love Lucy" on a computer tablet -- because the preceding match in Arthur Ashe Stadium lasted more than four hours: 2001 U.S. Open champion Lleyton Hewitt's 6-4, 5-7, 3-6, 7-6 (2), 6-1 comeback victory over 2009 champion Juan Martin del Potro.
Williams has dropped a total of eight games through six sets this week. Against Shvedova, she produced a 22-3 edge in winners. Williams faced only one break point, erasing it with one of her six aces, then following up with another clocked at 119 mph.
As for facing Stephens on Sunday, Williams said: "I definitely look forward to it. Whatever happens ... an American for sure will be in the quarterfinals, which is really good."
Much, much earlier, Stephens reached the round of 16 in New York for the first time by beating 23rd-seeded Jamie Hampton 6-1, 6-3 in another all-American matchup.
"Serena is the No. 1 player in the world. She's possibly the greatest player of all time. Sloane is Sloane. You know, she's making her own name. She's top 20 in the world for a reason," Hampton said. "They're both great players, both great competitors."
They've played twice in the past -- both in January, both on hard courts, both in the quarterfinals. First, Williams won 6-4, 6-3 at the Brisbane International. Three weeks later, Stephens came back for a 3-6, 7-5, 6-4 victory in Melbourne, where Williams was dealing with an ankle injury.
"You got to ... think about what you can do, how you can be better," Williams said about remembering what happened in Australia. "I'm sure she (thinks about) it as well -- how she did, how she can repeat that."
One thing to remember about Williams: She reacts well to disappointments.
Since her first-round loss at last year's French Open, Williams has won 94 of 99 matches and earned 13 titles, including championships from three of the past five Grand Slam tournaments.
"She's very aggressive. She stays on top you of you. Doesn't give you any room to breathe. She's intense. She knows what she wants to do out there. That's why she's No. 1," said Stephens, whose late father, John, was the 1988 NFL Offensive Rookie of the Year with the New England Patriots.
Stephens' impressive Grand Slam season includes her semifinal appearance at the Australian Open, and a quarterfinal run at Wimbledon. She lost to the eventual champion at both.
In all, she is 15-3 at major tournaments this year, but only 17-15 at lesser events, with six first- or second-round exits.
"The Grand Slams -- it's just showtime, I guess," Stephens said, shrugging her shoulders. "What can you do?"