French Open champion Ashleigh Barty is three victories away from becoming the first Australian woman since 1976 to top the singles rankings.
The dynamic 23-year-old landed her first grand slam title at Roland Garros earlier this month, and world number one Naomi Osaka's early exit from the Birmingham Classic has opened the door for Barty to nudge above the Japanese player.
Osaka crashed out in the last 16 on Thursday when she lost 6-2 6-3 to Kazakhstan's world number 43 Yulia Putintseva, suffering a blow to her preparations for Wimbledon on the Edgbaston grass.
Second seed Barty sailed through to the quarter-finals as a 6-3 6-1 winner against American Jennifer Brady but must capture the title on Sunday to depose Osaka.
Evonne Goolagong Cawley was the first Australian to reach number one on the WTA list, taking top spot away from Chris Evert for a fortnight in 1976, just six months after the computerised ranking system was introduced to the tour.
Venus Williams is no stranger to the summit of the rankings and the 39-year-old American remains a force to be reckoned with, particularly on grass.
The five-time Wimbledon champion is making her debut at this tournament and set up a quarter-final against Barty by beating China's Qiang Wang 6-3 6-2.
Germany's Julia Goerges, the eighth seed and a Wimbledon semi-finalist last year, was a 6-4 6-3 winner against Russian Evgeniya Rodina.