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The move came as TMZ Sports reported Azarenka will skip this year's US Open because of a custody battle over eight-month-old son Leo following a split last month with the boy's father, Billy McKeague.
The website said a judge in Los Angeles, where McKeague filed custody papers, will not allow the boy to leave California until the matter is settled, not expected until October.
That would prevent him from joining his mother in Cincinnati or at the US Open, which begins on August 28 in New York.
Azarenka, a 28-year-old from Belarus, cited personal reasons for skipping Cincinnati.
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"I am disappointed to have to pull out of the Western and Southern Open due to a family matter," she said. "I look forward to coming back to Cincinnati and playing in front of its great fans for many years to come."
Azarenka, ranked 203 after a layoff while pregnant and after her son's birth, played last month at Wimbledon, reaching the round of 16 before losing to second-ranked Simona Halep.
Cilic, the 2014 US Open champion from Croatia, pulled out with an adductor injury that has sidelined him since Wimbledon, where he lost in the final to Roger Federer.
"I was really eager to play in Cincinnati, where I won my first career ATP Masters 1000 singles title last year and where I had one of the best performances during my career," Cilic said.
"But I still don't feel at 100 percent to compete at the top level and to defend my title there."