Second seed and French Open champion Rafa Nadal has been named on the same side of the draw with seven-time winner Roger Federer of Switzerland.
Murray, who ended Britain's 77-year wait for a men's singles champion in 2013, is seeded third for the grasscourt championship, two places above his world ranking, and will meet David Goffin of Belgium on center court on Monday.
Should he reach the final four he could meet Serbian Djokovic, who will face Andrey Golubev of Kazakhstan, also on Monday.
Nadal opens his campaign against Slovakia's Martin Klizan on Tuesday, and faces a potential tricky second round match-up with Czech Lukas Rosol, who beat him in the second round two years ago.
Fourth seed Federer opens against Paolo Lorenzi of Italy, also on Tuesday.
In the women's draw, world number one Serena Williams could meet French Open winner Maria Sharapova in the last eight after they were drawn in the same quarter.
Five-times winner Williams meets Anna Tatishvili in the first round, while Sharapova plays British wildcard Samantha Murray.
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