Top-seeded Novak Djokovic was upset in the quarterfinals on Friday in the BNP Paribas Masters at Paris and could lose his world No. 1 ranking as a result.
Djokovic lost in straight sets to ninth-seeded Marin Cilic of Croatia 6-4, 7-6 (2) to end his bid for a fifth title at this tournament.
The surprising defeat -- Djokovic's first to Cilic in 15 career matches -- also could end the Serbian's 122-week reign atop the rankings.
Murray will supplant Djokovic at No. 1 if he beats the winner of Friday's late match -- Jo-Wilfried Tsonga or Milos Raonic -- in the semifinals.
"I've never been in this position before. I don't know how I'll deal with it," Murray said. "Normally in big matches, when you go on court, you feel fine. If I wasn't to get to No. 1 this year, I was looking to next year. If it happens, great. It's been a great few months for me and I'll try to finish this week the best I can."
Murray, 29, would also become the second-oldest player to reach No. 1 for the first time, behind John Newcombe, 30, in 1974.
"He's definitely a player who deserves that," Djokovic said of Murray. "To see how he has raised his level in the last 12 months is quite extraordinary."
Cilic, who clinched a spot in the season-ending Barclays ATP World Tour Finals with his victory on Thursday, next faces John Isner in the semifinals.
Isner outlasted fellow American Jack Sock 7-6 (6), 4-6, 6-4. Isner blasted 17 aces en route to reaching the semifinals at a Masters 1000 tournament for the first time since April 2015.