British number two Cameron Norrie will play three-time Grand Slam winner Stan Wawrinka at Queen's Club on Monday.
Andy Murray, making his comeback after a year out with a hip injury, plays Australian Nick Kyrgios on Tuesday at the Fever-Tree Championships.
Kyle Edmund, who has replaced Murray as British number one, meets American Ryan Harrison the same day.
Twelve-time major champion Novak Djokovic faces Australian qualifier John Millman, also on Tuesday.
Fifteen of the world's top 30 male players, plus Murray, Djokovic and Wawrinka, are competing in the west London tournament, although 18-time Slam champion Rafael Nadal and world number four Juan Martin del Potro have withdrawn.