Britain's Andy Murray is one win from becoming world number one following Novak Djokovic's surprise defeat by Marin Cilic at the Paris Masters.
Djokovic needed to reach the final to retain the top ranking but lost 6-4 7-6 (7-2) to Cilic in the quarter-finals.
Second seed Murray beat Czech Tomas Berdych 7-6 (11-9) 7-5 and will play Canadian Milos Raonic in Saturday's semi-final at about 15:30 GMT.
Victory would see the Scot top the rankings for the first time.
Murray claimed the first set after a thrilling tie-break in which he defended a total of seven set points, having at one stage been 6-1 down.
He immediately broke Berdych's serve in the second set, and looked set to force home his advantage until, when serving for the match at 5-4, his opponent broke back.
However, Berdych failed to take advantage and his double fault handed the initiative back to Murray, who held his nerve for a sixth successive win over the 31-year-old.
"Before the match there were a few more nerves maybe than there was earlier in the week," said Murray. "But once I got out there, I didn't feel any different to any other match.
"If it happens this week, great. But if not, I'm not putting any extra pressure on myself this week because I still think I have an opportunity to do it in the future.
"But obviously I'd love to do it tomorrow if I can."
Murray's semi-final is scheduled on court not before 15:30 on Saturday.
Should he reach the final in Paris, he will become the second-oldest player to debut at number one, after the 30-year-old Australian John Newcombe in 1974.
The Briton would also set a record for the most time between becoming number two and number one, having first reached number two in 2009.
Fourth seed Raonic beat France's 11th seed Jo-Wilfried Tsonga 6-2 7-6 (7-4) to set up a repeat of July's Wimbledon final, which Murray won in straight sets - his seventh win in a row against the Canadian.
Croat Cilic and American John Isner will contest the other semi-final at 13:00.
Friday's results meant Austrian Dominic Thiem became the eighth and final qualifier for the ATP World Tour Finals in London, joining Djokovic, Murray, Stan Wawrinka, Raonic, Kei Nishikori, Gael Monfils and Cilic.
'Murray deserves it' - Djokovic
Back in June, Djokovic beat Murray in the French Open final to complete a career Grand Slam. Now Murray is on the brink of ending the Serb's 28-month run as world number one.
Cilic had lost all 14 of his previous matches against Djokovic but made all the running in their 15th meeting, breaking serve twice in the first set and denying the top seed when he served for the second set.
Djokovic saw off two match points with a volley and a forehand winner but could not contain the more aggressive Cilic in the tie-break.
Asked about Murray possibly overtaking him as number one, Djokovic said: "He's definitely a player who deserves that.
"To see how he has raised his level in the last 12 months is quite extraordinary.
"We have known each other since very, very early days. We were, I think, 11 years old when we first played against each other. Undoubtedly, much respect for what he has done."
Russell Fuller, BBC tennis correspondent:
Murray admitted to an extra bout of nerves before taking the court to play Berdych, but says they soon evaporated once he settled into the rhythm which has served him so well in recent months.
He has won his last seven matches against Raonic - including the Wimbledon final - but this semi-final will present a unique challenge.
The world number one ranking is highly prized in tennis, and only 25 men have claimed the top spot since computerised rankings were introduced in 1973.