Davies, 54, would become the oldest champion in LPGA history if she wins.
“I’ll certainly have a crack at it,” said Davies, who carded one eagle and seven birdies on day three in Arizona. “I’ve given myself a chance.”
South Korea’s Park, who has nine wins in 15 attempts when leading into the final round, also hit a nine-under 63.
She is on 14 under, with Colombia’s Mariajo Uribe one shot back in second and third-placed Ariya Jutanugarn of Thailand on 12 under.
Davies’ hopes of registering a first LPGA win since 2001 could be hindered by a sore left calf and Achilles tendon.
“It’s a struggle,” she said. “It’s just walking. Swinging is fine. I can swing as hard as I want to. But every step is just misery.”
The oldest LPGA winner is Beth Daniel, who was 46 when she won the 2003 Canadian Women’s Open.
