British No 1 Kyle Edmund will play Jaume Munar of Spain in the first round at Wimbledon next week.
Edmund is seeded 30th and could play seventh seed Stefanos Tsitsipas in the third round.
Of the other Brits, a second-round tie against eight-time winner Roger Federer could be in the offing if Jay Clarke can get past American Noah Rubin.
Paul Jubb, the 19-year-old wild card, will make his Wimbledon debut against Portugal's Joao Sousa - with a second-round match against former finalist Marin Cilic possibly awaiting the winner.
Dan Evans and James Ward will play each other if they can beat Federico Delbonis and Nikoloz Basilashvili in their first round matches respectively.
Cameron Norrie starts his campaign against Denis Istomin, eighth seed Kei Nishikori may lie in wait in the second round.
Defending champion Novak Djokovic will open his campaign against Philipp Kohlschreiber for the first match on Centre Court on Monday.
Federer opens against South Africa's Lloyd Harris while his old rival Rafael Nadal has the most eye-catching draw, with a second-round clash against Nick Kyrgios looming, assuming he beats Japan's Yuichi Sugita.
Federer and Nadal could meet in the semi-finals after both were drawn in the same half.
Nadal was unhappy about being seeded below Federer in a reversal of their world rankings, but ultimately it has made no difference, with both in the opposite half to top seed Djokovic.
If the seedings pan out, the quarter-finals could see Djokovic against Tsitsipas while Kevin Anderson, last year's runner-up, could face Alexander Zverev on one side of the field - plus Federer vs Nishikori and Nadal vs Dominic Thiem in a French Open final rematch.
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