It will be the earliest meeting between the two since their first professional match in the second round of the 1998 Australian Open.
Tennis fans expressed frustration that the players weren't getting better crowds.
Serena had said on Monday that she "can't wait for the future" as she warmed up for her return to the WTA Tour at the Tie Break Tens exhibition at Madison Square Garden.
A summary of Friday's tennis action from around the world.
Former world number one Serena Williams looked sharp in her return to the hardcourts after a week-long break, soundly defeating Daria Gavrilova 6-1, 6-2 on Monday to advance to the second round of the Cincinnati Masters.
Images from Day 6 of the Australian Open in Melbourne on Saturday.
Naomi Osaka eased into the second round of the Italian Open on Monday with a 6-0, 6-3 victory over former world number one Victoria Azarenka, on a day in which local favourite Roberta Vinci called time on her career.
From Sania Mirza to Virat Kohli, even the likes of Virender Sehwag has shown that swagger on the runway.
Looking at the winners of the big night.
Germany's Angelique Kerber breezed past American Madison Keys in straight sets to enter the Australian Open semi-finals in Melbourne on Wednesday. The 2016 champion easily won 6-1, 6-2 in just 51 minutes.
The 2016 champion's next opponent may be far more to her liking than Hsieh, whose dazzling marksmanship left Kerber shrieking in frustration throughout much of the two-hour and eight-minute clash.
Summary of sports events and persons who made news on Thursday
He leads the men's seedings ahead of defending champ Roger Federer, with Bulgarian Grigor Dimitrov seeded third.
Sloane Stephens's US Open win could be the first of many Grand Slam titles for the young American, but there is a question mark on her ambitions, according to former world number one Mats Wilander.
"Sloane is truly one of my favourite people and to get to play her was really special," said Keys.
US Open champion Sloane Stephens said she has no pity for Madison Keys after thrashing her 6-3, 6-0 in Saturday's final, given the huge runnersup check her friend will receive.
Factbox on American Sloane Stephens, who beat compatriot Madison Keys 6-3 6-0 to win her first U.S. Open singles title on Saturday:
Keys is expected to be the aggressor on Arthur Ashe Stadium against a more defensive Stephens, one of the best retrievers on the tour.
Sloane Stephens watched January's Australian Open from her couch, a large cast on her left foot rendering her immobile and raising questions in her mind about her ability to bounce back from the injury.
The success of the American women at this year's US Open is nothing else than a reward from the Williams sisters' inspiration
Venus Williams will take on compatriot Sloane Stephens in one semi-final before her fellow Americans Madison Keys battles it out with CoCo Vandeweghe in the other in all-American semi-final in the women's singles at the US Open.
IMAGES from matches on Day 10 at the French Open at Roland Garros
Roger Federer and Rafael Nadal are just one step away from a US Open semi-final clash but both face tricky challenges to set up what would be their maiden encounter at Flushing Meadows.
The 37-year-old has enjoyed a renaissance season that has seen her reach the Australian Open and Wimbledon finals and sit just one victory away, against American compatriot Sloane Stephens, from playing for the US Open title for the first time since 2002.
Here are five things to watch for on day eight of the US Open on Monday.
Lindsay Davenport hailed Serena Williams for delivering a 'powerful message' that shows it is possible to 'pursue personal goals even when you're a mum'.
Rafael Nadal swept into the quarter-finals of the Italian Open on Thursday with a ruthless 6-4, 6-1 victory over Canadian teenager Denis Shapovalov. The top seed, who will reclaim the world number one ranking from Roger Federer if he wins his eighth title in Rome, turned in a near-flawless performance, losing only five service points as he honed in on victory in an hour and 22 minutes.
Thursday's match was just Venus Williams's seventh of the year and first since January's Australian Open, where she fell to Simona Halep in the round of 32.
Zverev defeated Anderson 6-4, 6-4 and captured his fourth title of the year in the finals played on Sunday.
He was nearly within striking distance of Nassar before court guards tackled him roughly to the ground in front of his shocked daughters.
Check out the most shocking upsets at this year's Wimbledon.
Ukrainian second seed Elina Svitolina ended Naomi Osaka's remarkable recent run with a 6-4, 6-2 triumph over the Indian Wells champion in the second round of the Miami Open on Friday.
Images from Day 8 of the Australian Open in Melbourne on Monday.
Images from the Australian Open in Melbourne on Thursday.
Unseeded Sloane Stephens crushed fellow-American Madison Keys 6-3, 6-0 to win her maiden Grand Slam, in the US Open final, in New York on Friday.
Keys and Stephens to put friendship to grand slam test
A rampaging Madison Keys completed an American sweep of the US Open women's quarter-finals on Wednesday, dismissing Estonia's Kaia Kanepi 6-3, 6-3 to guarantee an American champion at the year's final Grand Slam.
Venus Williams's renaissance year continued on Tuesday when she downed Petra Kvitova 6-3, 3-6, 7-6(2) in an electrifying atmosphere to set up an all-American US Open semi-final against Sloane Stephens.
Security worries could create a tense atmosphere at the French Open this year after a bomb attack on a British concert hall killed 22 people, French tennis player Lucas Pouille said.
Here are some of the best moments from the 'event-of-a-lifetime.