The Briton, 29, will face France's Jo-Wilfried Tsonga, who beat Croatian Ivo Karlovic 5-7 7-5 7-6 (8-6), on Sunday.
Murray will usurp Novak Djokovic as number one with titles in Vienna and at next week's Paris Masters, if Djokovic does not reach the final in Paris.
The Scot has never been top of the world rankings.
Murray has won 13 of his 15 matches against Tsonga, including a last-16 victory in their most recent meeting at Wimbledon in July.
Tsonga came from a set and 4-2 down in the second set to beat Karlovic, saving a match point in the tie-break as he reached his first World Tour final of the year.
courtesy - BBC