Djokovic's half of the draw also includes a potential semi-final against either fourth seed Kei Nishikori, last year's US Open runner-up from Japan, or defending champion Marin Cilic.
The other half, paced by second seed Roger Federer, includes the Wawrinka-Murray possible last-eight meeting.
Federer could meet Czech Tomas Berdych in the quarter-finals and might meet John Isner in the round of 16.
Former champion Murray was drawn to face controversial Australian Nick Kyrgios in the first round.
Kyrgios, 20, was handed a suspended ban and fine this week for his lurid verbal attack on Stan Wawrinka at the Montreal Masters.
World number 37 Kyrgios triggered widespread revulsion for his on-court taunt that fellow Aussie Thanasi Kokkinakis had had a fling with WTA professional Donna Vekic, reportedly the girlfriend of Wawrinka.