Defending champion Andy Murray could face top-seeded Novak Djokovic only in the U.S. Open semifinals, while Rafael Nadal and Roger Federer - who have never played each other at Flushing Meadows - might meet in the quarterfinals.
Murray beat Djokovic in the 2012 final.
Thursday's draw for the year's last Grand Slam tournament also set up these possible men's quarterfinals: 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.
The potential women's quarterfinals 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.