Defending champion Williams, whose relationship with Stephens was strained after the prodigy upset the 16-time Grand Slam champion at Melbourne, advanced early Saturday by beating 78th-ranked Kazakh Yaroslava Shvedova 6-3, 6-1.
"It's going to be tough. Sloane is playing so well. I'm always so happy for her. She's doing great. I'm really proud of Sloane. It's going to be a really good match," Williams said.
US 15th seed Stephens eliminated US 23rd seed Jamie Hampton 6-1, 6-3, Friday and now faces the superstar she accused of disrespectful intimidation tactics and mind games for a quarterfinal berth on the Flushing Meadows hardcourts.
"It'll be epic and something a lot of people will be looking forward to. I'm excited about it," Stephens said.
Williams, who at 31 could become the oldest US Open women's champion, and Stephens have not played since the 20-year-old phenom beat the four-time US Open champion 3-6, 7-5, 6-4 in an Australian Open quarter-final last January.
Stephens was friendly with Williams a year ago at New York but the relationship soured after Williams beat her in a Brisbane quarter-final 6-4, 6-3 and then suffered the shock Grand Slam defeat.
Williams did not refer to Stephens by name after the Brisbane match and Stephens later derided that, plus her rival's loud screams of "Come on" during their matches and even that Williams had dropped off her list of Twitter followers.
Stephens now says the relationship has been repaired. "Love her. We're all good. We're competitors, co-workers. It's definitely tough but now we're in a good place. That's all old news now and we've moved on. We're fine. I think that's all that matters," Stephens said.


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