A wild card at the Spanish indoor hard court event, which he won in 2009, Murray is eighth in the race to secure a berth at the season-ending tournament in London.
The Scot will play top-seeded Spaniard David Ferrer, who is also eyeing a place at the Tour finals, on Saturday for a place in Sunday's showpiece.
Ferrer, chasing a fourth Valencia trophy after triumphs in 2008, 2010 and 2012, swept past Brazilian qualifier Thomaz Bellucci 6-1 6-2.
Friday's remaining two quarter-finals feature unseeded Frenchman Jeremy Chardy against Spanish wildcard Pablo Carreno Busta and an all-Spanish clash between unseeded pair Tommy Robredo and Pablo Andujar.
Murray is attempting to qualify for the Tour finals for a seventh consecutive year and won the Vienna title last week when he came from a set down to beat Ferrer in the final.
(Reporting by Iain Rogers, editing by Toby Davis)
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