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Murray, a two-time Wimbledon champion, has slipped to 156 in the world after only returning to action at Queen's last week following 11 months out with a hip injury.
The 31-year-old lost first up at Queen's but was buoyed by beating fellow three-time major winner Stan Wawrinka in the opening round at Eastbourne on Monday.
Murray suffered his hip injury in the quarter-finals at Wimbledon last year and underwent surgery in January.
This year's Wimbledon gets underway on Monday.