It will be the earliest meeting between the two since their first professional match in the second round of the 1998 Australian Open.
Reigning champions Novak Djokovic and Serena Williams have been named top seeds for the Australian Open starting on Monday.
Nadal faced no break points in a ruthless display to set up a meeting with Canadian Denis Shapovalov.
Venus Williams gained revenge for her Wimbledon final defeat by Garbine Muguruza when the American advanced to the last four of the WTA Finals with a gutsy 7-5 6-4 victory over the Spanish world number two on Thursday.
Images from the third day at the US Open, the final Grand Slam tournament of the year, in New York, on Wednesday:
Keys and Stephens to put friendship to grand slam test
World number one Naomi Osaka was beaten in her opening match at the Dubai Duty Free Tennis Championships on Tuesday, losing to France's Kristina Mladenovic 6-3, 6-3 on her return to competitive action after winning last month's Australian Open.
US Open, the final Grand Slam of the season, starts Monday, August 28, at Flushing Meadows in New York.
Roger Federer reached the Rogers Cup semi-finals on Friday after coming to the net early and often in a straight sets victory over Roberto Bautista Agut on a windy day in Montreal.
Venus Williams's encouraging form at the Australian Open has given younger sister Serena cause to look over her shoulder after the siblings eased into the third round with straight-sets wins at Melbourne Park on Thursday.
Leylah Fernandez's storybook US Open continued with yet another upset on Thursday, as the Canadian teenager shocked second seed Aryna Sabalenka 7-6(3), 4-6, 6-4 to reach her first Grand Slam final.
American Jennifer Brady defeated compatriot Coco Gauff 6-2, 6-4 at the Top Seed Open on Saturday, earning a spot in her first WTA final.
At one stage Yuki was a break up, serving for the opening set but lost his serve and eventually the set. After drawing parity, Yuki twice lost his serve to fall behind 0-3 in the decisive set and never recovered.
Andy Murray took a step closer to a first title in arguably the toughest year of his playing career, grinding out a 3-6, 7-5 ,6-2 win over Ugo Humbert on Saturday to reach the final of the European Open in Antwerp.
Andy Murray overcame a slow start and a third set service break to beat Taro Daniel 1-6, 6-2, 6-4 in the first round of Indian Wells on Friday and notch his 700th career win.
Former world number one Andy Murray won his first ATP tour singles match in nearly nine months with a 6-3, 6-7(6), 6-1 victory over American Tennys Sandgren in the opening round of the Zhuhai Championships.
Images from Day 4 of the French Open, at Roland Garros, in Paris.
World No 1 Serena Williams showed plenty of rust in her first competitive outing of the year ahead of the Australian Open, but battled through to defeat Andrea Petkovic in straight sets at the Brisbane International on Tuesday.
Shapovalov will meet Rafael Nadal for a place in the semi-finals.
Swiss seventh seed Belinda Bencic was stunned by Slovakia's Magdalena Rybarikova while former champion Ana Ivanovic was also sent packing in third-round action at the BNP Paribas Open in California.
The 16-times Grand Slam champion, who has been slightly ill lately, was kept on his toes before racing to victory to set up a meeting with seventh seed Stefanos Tsitsipas.
Top seed Serena Williams made short work of Kazakhstan's Zarina Diyas in the third round of the BNP Paribas Open.
Wimbledon debutant Eubanks ends Tsitsipas's challenge in fourth round.
Greek tyro Stefanos Tsitsipas' dream run at the Rogers Cup continued on Friday as the teenager toppled defending champion Alexander Zverev 3-6, 7-6(11), 6-4 to reach the semi-finals in Toronto.
It was Novak Djokovic's first match this year after his Australian Open hopes were dashed when he was deported following an 11-day saga revolving around his decision not to have a COVID-19 vaccination.
Serena Williams sounded a warning for her fellow Australian Open contenders with a sleek win
Klitschko and his brother Vitali, also a former world heavyweight champion and now the mayor of Kyiv, have both taken up arms against invading Russian forces.
Four times now, twice at Wimbledon (2018, 2019) and at the US Open (2018, 2019) Serena Williams has come agonizingly close to that 24th Grand Slam only to fall at the final hurdle.
Form guide for American Serena Williams ahead of Thursday's US Open semi-final clash against Latvia's Anastasija Sevastova:
A summary of Friday's tennis action from around the world.
Greek teenager Stefanos Tsitsipas slayed another tennis giant on Saturday, saving a match point as he toppled big-serving Kevin Anderson 6-7(4), 6-4, 7-6(7) in a thriller to set up a Rogers Cup final against top seed Rafael Nadal.
Rafael Nadal rallied from a set down to ease past Fabio Fognini 4-6, 6-1, 6-2 in the Italian Open quarter-finals on Friday and set up a mouth-watering clash against long-time adversary Novak Djokovic for a place in Sunday's final. Djokovic plotted a similar path to the Spanish clay-court king when the Serb lost the first set against Japan's Kei Nishikori before recovering to win 2-6, 6-1, 6-3 and seal an open-era record 51st career meeting against Nadal.
Defending champion Serena Williams is the top seed in the women's draw. The American will be looking to equal Steffi Graf's Open era record by sealing a 22nd Grand Slam triumph.
IMAGES from Australian Open matches played at Melbourne Park on Friday
Milos Raonic overcame third seed Grigor Dimitrov 7-5, 3-6, 6-3 to reach the third round at the Madrid Open on Tuesday and set up an all-Canadian clash with teenager Denis Shapovalov.
World number two Simona Halep beat Maria Sharapova 6-2, 6-2 in the China Open third round on Wednesday for her first win over the Russian in eight attempts.
Bernard Tomic is set to sit out the Australian Open after Tennis Australia (TA) decided not to award him a wildcard to the main draw, the organisers said on Thursday.
Images from Day 5 of the US Open in New York on Friday
Top seeded Ash Barty overcame a slow start to defeat Maria Sharapova 6-4 6-1, while Simona Halep battled past Ekaterina Alexandrova 3-6 7-5 6-4 in the second round of the Cincinnati Masters on Wednesday.
Images from the Australian Open matches played at Melbourne Park on Wednesday.
