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Murray earned his first Grand Slam championship by beating Djokovic in the 2012 US Open final, then added a second by beating him in the Wimbledon title match last month. But there can't be a rematch in New York in the final, thanks to Thursday's draw.
"Coming to the US Open last year, I'd never won a Grand Slam. I didn't know if I was ever going to win one," Murray said at the draw ceremony. "A lot of people would say ... 'He's good enough to win a Grand Slam. He's going to win one.' But the more finals you lose in, the more you start to doubt yourself and think, 'Is it ever going to happen?' Getting that weight off my shoulders last year was huge."
Play at the year's last Grand Slam tournament begins on Monday.
In addition to No 2 Nadal against No 7 Federer, a 17-time major champion who has his lowest seeding at the US Open since 2002, the other possible men's quarterfinals are 2011 champion Djokovic vs. 2009 champion Juan Martin del Potro, No 3 Murray vs. No 5 Tomas Berdych, and No 4 David Ferrer vs. No 8 Richard Gasquet.
Federer, who has won five U.S. Open titles, and Nadal also were set up for a possible quarterfinal at Wimbledon this year, but that never materialized: Nadal lost in the first round, and Federer in the second.
The potential women's quarterfinals at the US Open are No 1 Serena Williams against No 8 Angelique Kerber, No 2 Victoria Azarenka against No. 7 Petra Kvitova, No. 3 Agnieszka Radwanska against No 5 Li Na, and No 4 Sara Errani against No 6 Caroline Wozniacki.
The woman who originally was seeded third in the tournament, 2006 champion Maria Sharapova, withdrew Wednesday because of a right shoulder injury.
Williams' 16 Grand Slam titles include four at the US Open, including last year. Her first-round opponent will be 2010 French Open champion Francesca Schiavone. Williams could play 15th-seeded Sloane Stephens of the United States in the fourth round; Stephens won their Australian Open quarterfinal in January.
Williams has won 77 of her past 81 matches, and was asked on Thursday whether she is playing better than she ever has.
"I hope not," Williams answered. "I always like to hope I can do better, so we'll see."
Her older sister, 2000-01 US Open champion Venus, is unseeded and was drawn to play No 12 Kirsten Flipkens, a Wimbledon semifinalist last month, in the first round.
Djokovic and 2010 US Open champion Nadal, who recently overtook Murray at No 2 in the rankings, could meet only in the final. They've already met in five Grand Slam championship matches, including in New York in 2010 and 2011.
One intriguing earlier matchup for 12-time major title winner Nadal could come in the fourth round, when he might have to play big-serving American John Isner, who is seeded 13th and pushed the Spaniard to five sets at the French Open two years ago.
Nadal was drawn to play another American, 21-year-old Ryan Harrison, in the first round.
Djokovic, who has reached at least the semifinals at the US Open each of the past six years, could face 25th-seeded Grigor Dimitrov in the third round. Dimitrov surprisingly beat Djokovic on clay at the Madrid Masters in May, although Djokovic won their matchup less than a month later at the French Open.
In the second round, Djokovic might play Lukas Rosol, the man who upset Nadal at Wimbledon while ranked 100th in 2012, or Benjamin Becker, who defeated Andre Agassi at the 2006 US Open in the American's last professional match.
