A shoulder injury which forced Serena Williams to abandon the Cincinnati Open may topple her from the world number one ranking this week.
Second seed Angelique Kerber will replace Williams at the top of the standings if she wins the tournament.
Williams, 34, had last week accepted a wild card to defend her title after playing at the Olympic Games in Rio.
“My shoulder inflammation continues to be a challenge, but I am anxious to return as soon as possible,” she said.
The American withdrew following a practice session on Monday.
Williams has been ranked world number one for 183 consecutive weeks, and 306 in total.
She was knocked out of the Olympics in the third round by Ukrainian Elina Svitolina, and was beaten in the doubles with sister Venus in the first round – their first defeat in 16 Olympic matches together.
The US Open, the final Grand Slam of the year, begins on 29 August.