The defending champion and No. 2 seed can reach his third straight final at Flushing Meadows without having to face either Roger Federer or Andy Murray. Those two, meanwhile, could meet in the semifinals for a rematch of their recent finals at Wimbledon and the Olympics.

‘‘It’s a question of luck,’’ Djokovic said when asked about the only true drama in the unveiling of the bracket — whether third-seeded Murray would end up on his or top-seeded Federer’s side of the draw. ‘‘You try to focus on what’s in your hands, what’s in your power. Thinking about the semifinal at this moment, I don’t think it’s the best thing.’’

In the women’s bracket, third-seeded Maria Sharapova drew a possible semifinal matchup against top-seeded Victoria Azarenka and fourth-seeded Serena Williams could play No. 2 Agnieszka Radwanska in the semifinals.

Rafael Nadal, ranked third, is out of this year’s tournament with a knee injury, marking the first time since 2008 that the quartet of Federer, Nadal, Djokovic, and Murray haven’t been seeded 1 through 4 in some order at the US Open.

Taking the fourth seed this year is David Ferrer, who has never made a Grand Slam final, and could face Djokovic in the semifinals.

Of the 16 semifinal spots over the last four Grand Slam tournaments, 14 have been occupied by one of the big four.

No American man has won the US Open since Andy Roddick in 2003. There are four seeded US men trying to halt that streak: No. 9 John Isner, No. 23 Mardy Fish, No. 27 Sam Querrey, and Roddick, who is seeded 20th.

Sharapova completed the career Grand Slam at the French Open this year, while Williams has 14 Grand Slam titles and is coming off wins at Wimbledon and the Olympics.

Williams’s older sister Venus, who is ranked 47th this week and not seeded, plays American wild-card entry Bethanie Mattek-Sands in the first round. Venus, the 2000 and 2001 champion, pulled out of last year’s US Open hours before she was scheduled to play in the second round, revealing that she had been diagnosed with an auto-immune disease.

Four-time major champion Kim Clijsters will begin what she says will be the last tournament of her career against American wild-card recipient Victoria Duval. Clijsters, seeded 23d, might face the defending champion, seventh-seeded Sam Stosur, in the fourth round.