The American last occupied top spot in the rankings 15 years ago, but could make a return by winning the WTA Finals title.
WTA Finals: Williams books semi-final place to stay in No 1 hunt, Pliskova struggles for motivation in defeat to Ostapenko
Venus Williams claimed a measure of revenge on Garbine Muguruza by defeating the Spaniard at the WTA Finals to take her place in the last-four and remain in the hunt for a remarkable return to the top of the rankings.
Williams was beaten by Muguruza in the Wimbledon final in July, but she proved too strong for her opponent in Singapore, prevailing 7-5, 6-4 to advance from the White Group and eliminate Muguruza in the process.
It was Williams' first win over Muguruza in three attempts this year having also lost to her in the Rome Masters quarter-finals.
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"What can I say, I was playing an amazing opponent. She has had an amazing year," Williams said. "I was just so happy to win the last point.
"It's not easy out here. You have to play every point well or else you find yourself losing the game. I had some great coaching going into the match, so thanks to my team, and I hope we can win some more."
Despite a straight sets victory, it was not a straightforward result for Williams, who was the first to be broken in the opening set to trail 3-4, only to respond immediately with a break of her own.
Williams then earned the all-important second break in the 12th game, closing out the set at the third attempt.
A topsy-turvy second set began with three successive breaks of serve before Muguruza held in the fourth game to take a 3-1 lead. Williams responded to level at 3-3, but handed the advantage back for Muguruza to lead 4-3.
That advantage lasted just one game as Williams fought back to win the next three games to seal the victory.
Williams takes her place in the semi-finals alongside White Group winner Karolina Pliskova, who lost her final group match to the already-eliminated French Open champion Jelena Ostapenko.
Williams' presence in the WTA Finals last-four continues an impressive season for the 37-year-old American, who reached two grand slam finals and returned to the top five in the world rankings.
Williams also remains in the running for a return to world No 1, more than 15 years after she last held the top ranking.
"I use a lot of sun protection, I eat a lot of fruit and vegetables, and that's been the key to my success," Williams jokingly said when asked about the cause of her longevity.
While it was all smiles and laughter from Williams following her win, Pliskova said she struggled for motivation in her defeat to Ostapenko.
Having already booked her place in the semi-finals, the Czech world No 3 fell to a 6-3, 6-1 loss to Ostapenko, the world No 7 from Latvia.
"It was really tough to push myself and play my best tennis when you know you've qualified," Pliskova, 25, said. "I haven't ever been in this situation. I didn't know how I was going to feel and how she was going to play. I think she played amazing."
Despite the setback, Pliskova remained confident of bouncing back in her semi-final tomorrow.
"I think it will now feel like a normal tournament," she said. "Hopefully I'll be ready, and I'm sure I'm going to feel much better and play much better."
The WTA Finals group stage concludes on Friday, with Romanian world No 1 Simona Halep taking on Elina Svitolina, the world No 4 from Ukraine, and Frenchwoman Caroline Garcia, ranked No 8, facing world No 6 Caroline Wozniacki from Denmark.
There is still all to play for in the Red Group, with Wozniacki the only player assured of her place in the semi-finals.