WIMBLEDON, England — Roger Federer and Rafael Nadal were set up for a potential semifinal at Wimbledon in Friday’s draw, while Serena Williams was placed in what shapes up as by far the toughest quarter of the women’s field.

With defending champion Novak Djokovic in the top half of the men’s bracket, the No. 2-seeded Federer and No. 3-seeded Nadal were placed together in the bottom half. Nadal is ranked No. 2, and Federer No. 3, but that was reversed by Wimbledon’s seeding system, which takes into account grass-court results over the past two years.

The possible men’s quarterfinals are No. 1 Djokovic against No. 7 Stefanos Tsitsipas, and No. 4 Kevin Anderson, last year’s runner-up, against No. 6 Alexander Zverev on one side of the field, and Federer vs. No. 8 Kei Nishikori, and Nadal vs. No. 5 Dominic Thiem on the other. Nadal-Thiem would be a rematch of the 2018 and 2019 French Open finals, both won by Nadal.

The women’s quarterfinals could be No. 1 Ash Barty vs. No. 5 Angelique Kerber, the defending champion; No. 3 Karolina Pliskova vs. No. 8 Elena Svitolina; No. 2 Naomi Osaka vs. No. 7 Simona Halep; No. 4 Kiki Bertens vs. No. 6 Petra Kvitova, the two-time champion who must decide whether to play after being sidelined with an injured left forearm.

Williams, a seven-time champion at the All England Club and owner of 23 Grand Slam titles in all, might face Kerber in the fourth round — a rematch of their 2018 Wimbledon final and 2016 Australian Open final, both won by Kerber —  and then French Open champion Barty in the quarterfinals.

That section of the field also includes past Wimbledon champions Garbiñe Muguruza and Maria Sharapova, and strong grass-court players Julia Goerges, Belinda Bencic, Donna Vekic, Kaia Kanepi and Alison Riske. Kerber could meet Sharapova in the third round.

At least Williams, who as usual skipped the grass-court tuneup events, gets a chance to work herself into form. She opens against a qualifier, 162nd-ranked Giulia Gatto-Monticone of Italy, then could face another qualifier in the second round.

The most intriguing first-round matchup in either the men’s or women’s bracket involves the other Williams sister: Venus, 39, will take on 15-year-old American Coco Gauff, the youngest qualifier at the All England Club in the half-century Open era.

Nadal starts off against qualifier Yuichi Sugita of Japan, and Federer’s first opponent is Lloyd Harris, a 22-year-old South African making his Wimbledon debut. Djokovic will get things going in Centre Court on Monday against Philipp Kohlschreiber, a former top-20 player who was a 2012 quarterfinalist at Wimbledon and beat Djokovic on a hard court at Indian Wells, California, this year.