Then Stephens — and the tennis world — needed to wait several hours to find out whether Williams would, too.
From the moment the women's draw came out at Flushing Meadows, it was clear which potential fourth-round match was the most intriguing: defending champion Williams against up-and-coming talent Stephens.
"It's something I think everyone is looking forward to," Stephens said.
On a ho-hum afternoon devoid of any truly significant surprises, Stephens reached the round of 16 in New York for the first time by beating 23rd-seeded Jamie Hampton 6-1, 6-3 Friday.
Williams, seeking her fifth U.S. Open title, was scheduled to face 78th-ranked Yaroslava Shvedova of Kazakhstan at night, after things came alive a bit thanks to 2001 champion Lleyton Hewitt's stirring 6-4, 5-7, 3-6, 7-6 (2), 6-1 comeback victory over 2009 winner Juan Martin del Potro.
It was the ninth time in the past 10 years that two previous title winners faced each other in New York; Hewitt was a participant in three of those in the past, going 0-3.
The 32-year-old Australian, a former No. 1 now ranked 66th after a series of injuries, repeatedly scrambled along the baseline to come up with passing winners against the sixth-seeded del Potro.
"I don't know how many years I've got left in me. I keep getting asked the question," said Hewitt, who won Wimbledon in 2002. "I'm just pumped to get out on this court and try to put on a great show."
Earlier, two other U.S. Open winners, defending champion Andy Murray and top-seeded Novak Djokovic, experienced only brief lulls before staying on course for a possible showdown in the semifinals.
About 40 minutes into his match, Djokovic faced two set points, but he erased those thanks to errors by his opponent, and after adjusting to the swirling wind, wound up defeating 87th-ranked Benjamin Becker 7-6 (2), 6-2, 6-2. Murray dropped a set, yelled at himself after some awkward miscues, but finished well, taking the last five games of his 7-5, 6-1, 3-6, 6-1 victory over 81st-ranked Leonardo Mayer of Argentina.
Becker, who beat Andre Agassi at the 2006 U.S. Open in the final match of the American's career, "is a quality opponent, and he should have won the first set," Djokovic acknowledged. "I was fortunate enough to come back and win the first set, and after that, I was much more comfortable on the court."
During the day session, the only seeded man to bow out was No. 17 Kevin Anderson, a 6-2, 6-2, 6-2 loser against 2006 Australian Open finalist Marcos Baghdatis, while all seven women's matches were decided in two sets. Winners included 2011 French Open champion Li Na, 2012 Wimbledon runner-up Agnieszka Radwanska, and 2008 U.S. Open runner-up Jelena Jankovic.
Toronto's Daniel Nestor and Vasek Pospisil of Vernon, B.C., beat the Spanish pair of Albert Montanes and Tommy Robredo 4-6, 6-2, 6-1 in the men's doubles tournament.
The buzz already was building about Williams vs. Stephens, even before Williams faced Shvedova.
"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."
Hampton's blase summation of a possible Williams-Stephens matchup: "I don't really make too much of it."
She might be the only one.
Williams is 32, seeded No. 1, and owns 16 major titles. Stephens is 20, seeded 15th, and already carrying the label of "Next Big Thing" in American tennis. Not only that, but Stephens surprisingly won their Australian Open quarter-final in January, one of only four losses in 66 matches for Williams in 2013. Oh, 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. It's fine."
They've played twice in the past — both in January, both on hard courts, both in the quarter-finals. 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.
"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," Stephens said.
Thinking back to their previous matches, Stephens added: "It was very important for me the first time to just even get out there and be like, 'OK, it's not as scary as I thought it would be.' I think being able to have played her a couple times before, I'm excited to get back out there."
Stephens has reached at least the fourth round at all four Grand Slam tournaments this season, including a semifinal run at the Australian Open and a quarter-final berth at Wimbledon, losing to the eventual champion in both.
"She just likes the big matches, you know," the 23-year-old Hampton said. "She shows up to play at the Slams, for sure."
Stephens-Hampton was the first match in Arthur Ashe Stadium between two American women younger than 24 since the Williams sisters met in the 2002 final.
And Stephens dominated, in part because she handled the occasion far better than Hampton did. Both players finished with 12 winners, but while Stephens limited herself to 15 unforced errors, Hampton made 34.
Afterward, Hampton blamed her own jitters, saying she's been working with a sports psychologist to try to improve her mindset when the stakes are most significant.
"I've had tendencies, shown tendencies, to play really bad in big moments," Hampton said. "I'm incredibly, incredibly disappointed in the way I played today."
Stephens might say the same about how she shows up at lower-tier tournaments. While her Grand Slam record this season is 15-3, she is only 17-15 at other tournaments, with six losses in the first or second round.
"The Grand Slams — it's just showtime, I guess," Stephens said, shrugging her shoulders. "What can you do?"