Friday's match will be the earliest the sisters have met at a Slam since the 1998 Australian Open in what was also their first ever clash.
Two-time champion Venus beat Italy's Camila Giorgi 6-4 7-5.
It was another powerful performance from Serena Williams who beat German Carina Witthoeft in straight sets 6-2, 6-2 in the second round on Wednesday evening.
Serena Williams has responded to French Open officials criticizing her clothing at Roland Garros in the most Serena Williams way possible.
"Unfortunately and fortunately we have to play each other", said Serena, 36.
The 38-year-old American said the crowd's encouragement had helped her.
Serena is No. 26, playing in only the seventh tournament since she was off the tour for more than a year while having a baby.More news: Cyberpunk 2077 Gameplay Demo is Streaming on CD PROJEKT RED Twitch Channel
More news: Simona Halep suffers upset at US Open to Kaia Kanepi
More news: Meghan channels Hollywood style on 'date night' with Prince Harry
They've played each other in the finals of all four Slams, including at the US Open in 2001 (when Venus won) and 2002 (when Serena did).
US Open organisers said they "regret" that Cornet was given a code violation and had clarified their policy to "ensure this will not happen moving forward".
"You're beating it up now", the elder sister said.
Alize Cornet of France removed her top briefly during her first round at the 2018 US Open in New York, Aug. 28, 2018. "So I think it's fine". "So hopefully I'll see her Friday".
Just days after Billy Jean King criticized the French Open's tournament chief of "policing women's bodies" for saying Serena Williams' cat suit "would no longer be accepted", the U.S. Open came under fire after a female player was penalized for briefly removing her top on the court. Even though she was wearing a full coverage sports bra, which is routinely used in training, the umpire was not ready to give any leeway.
Azarenka, the 2012 and 2013 runner-up, made the third round for the first time in three years with a 6-1, 6-2 win against Australian 25th seed Daria Gavrilova.
"When you take that agency away from athletes.it says a lot about who feels they have control", McManus said. "Unsportsmanlike conduct.?? But the men can change shirts on court", tweeted Scottish tennis coach Judy Murray, who is the mother of professional tennis player Andy Murray.