Friday's draw for the grass-court Grand Slam placed the third-seeded Federer and No. 5 Nadal in the same half. Federer is the defending champion at the All England Club, while Nadal is a two-time winner.
Home favorite Andy Murray, who is seeded No. 2, is also in the same bottom half and could meet Nadal or Federer in the semifinal.
Top-seeded Novak Djokovic is in the top half and has a much easier path to the final, facing a possible semifinal against No. 4 David Ferrer.
Nadal and Federer have met in three Wimbledon finals but have never played each other before the semifinals of any Grand Slam tournament. In 2008, they played one of the greatest finals ever on the London grass, with Nadal prevailing 9-7 in the fifth set to claim his first Wimbledon trophy.
Last year, Federer won his record-tying seventh Wimbledon title by beating Murray in the final. Murray, who later beat Federer for the Olympic gold at Wimbledon, will be bidding to become the first British player to win the men's title since Fred Perry in 1936.
The other possible men's quarterfinals are: Djokovic against No.7 Tomas Berdych; Ferrer vs. No. 8 Juan Martin Del Potro and Murray against No.6 Jo-Wilfried Tsonga.
Wimbledon's seeding order is determined using the ATP rankings and points are added for achievements in grass-court tournaments over the past 12 months.
Nadal, coming off his eighth French Open victory, has been seeded No. 5 after being sidelined for about seven months with a left knee injury following his surprise loss in the second round at Wimbledon last year.
Nadal has looked unstoppable since his return from injury and the draw is certainly a tough one for Federer, who has recently showed signs of decline but bounced back with a victory in his favorite warm-up for Wimbledon, in Halle, Germany. Four of Federer's seven wins at Wimbledon came after he lifted the trophy in Halle.
But Nadal is also facing a daunting challenge, with the prospect of having to beat Federer, Murray and Djokovic to claim the title.
Nadal, who owns 12 Grand Slam titles, has a won-loss record of 43-2 in 2013, winning seven titles from nine finals and is on a 22-match winning streak. He has not played in an official tournament since the French Open after deciding to rest rather than play in Halle.
Earlier this week, Murray said he was not concerned about the draw, knowing that he would have to beat the best players in the field to end the British drought in Wimbledon.
"If you want to win the biggest tournaments, you have to beat the best players in the world," the US Open champion said. "It doesn't really matter where they are in the draw."
Federer, Nadal and Murray will all play on Monday's opening day at Wimbledon.
Federer will open the defense of his title against Victor Hanescu of Romania, while Nadal will take on Steve Darcis of Belgium and Murray plays Benjamin Becker of Germany, an opponent he beat last week at the Queen's Club.
Djokovic, who won Wimbledon two years ago, will start on Tuesday against Florian Mayer of Germany. He is guaranteed to keep the No. 1 spot in the ATP rankings after the tournament whatever the result he achieves.
There are several noteworthy first-round matchups in the men's draw, with former champion Lleyton Hewitt facing No. 11 Stanislas Wawrinka; No.21 Sam Querrey against Bernard Tomic; and No. 10 Marin Cilic playing Marcos Baghdatis.
In the women's draw, five-time champion and top-seeded Serena Williams will open against Mandy Minella of Luxembourg. Second-seeded Victoria Azarenka has a first-round match against Maria Joao Koehler of Portugal.
In the absence of her sister Venus, who pulled out this week with a back injury, Serena is bidding to win her 17th Grand Slam title and is considered the overwhelming favorite. Since losing in the first round at the French Open last year, she has amassed a record of 74-3 and won three of the last four major titles.
No. 3 Maria Sharapova, who lost to Williams in the French Open final, will open her Wimbledon campaign against Kristina Mladenovic. No.4 Agnieszka Radwanska will take on qualifier Yvonne Meusburger.
The possible women's quarterfinals are: Williams vs. No. 7 Angelique Kerber; Radwanska vs. No. 6 Li Na; Sharapova against No. 5 Sara Errani, and Azarenka vs. eighth-seeded Petra Kvitova.