Denmark's Wozniacki, 20, says that reaching world number one is her ambition
Top seed Caroline Wozniacki advanced to the Pan Pacific Open semi-finals after Agnieszka Radwanska retired with a foot injury in the first set.
At 5-0 down, sixth-seeded Pole Radwanska consulted with a trainer before deciding she could not continue.
Aiming for her sixth title in 2010, Dane Wozniacki will meet eighth-seeded Victoria Azarenka of Belarus on Friday.
Wozniacki could become world number one if she lifts the trophy and reaches the last four in next week's China Open.
If, however, the 20-year-old world number two does not overtake Serena Williams on this occasion, she believes other opportunities to be
officially recognised as the world's best
"If I reach number one that is great," Wozniacki said.
"It's always been a goal of mine - but if it doesn't happen this year there will be other chances."
Azarenka easily defeated United States qualifier Coco Vandeweghe in straight sets, 6-2 6-1.
In other matches at the tournament in the Japanese capital of Tokyo, French Open champion Francesca Schiavone beat Kaia Kanepi of Estonia 7-5 4-6 7-5.
Italy's Schiavone will meet seventh-seeded Elena Dementieva of Russia in the semi-finals. Dementieva beat compatriot and number two seed Vera Zvonareva 7-5 6-2.