After a second-round 68 at the weather-shortened Evian, she is in pole position to become her country's second major victor.
Moriya Jutanugarn's impressive year continued at the Evian Championship on Saturday as she moved in sight of her first LPGA title and maiden major success. Kirk won the Thornberry Creek LPGA classic earlier this year, her first win since 2010.
LPGA Tour officials, to the consternation of many, cancelled existing scores and made it a 54-hole tournament starting afresh on day two.
Rounds of 66 and 69 put her in a position to win her first major. But she went on to finish in a disappointing tie for 16th at St Andrews.
"That was a huge confidence boost, especially after struggling for a couple years and questioning whether I'd be playing much longer", said Kirk.
"But I reckon if I keep knocking on the door, one day it will be my turn", she said. "Hey, you know what, I can win out here, and just keep believing and keep doing the right things, and you never know what happens".
Announcing the decision to shorten the event yesterday, Ladies Professional Golf Association commissioner Mike Whan commented: "Some players will not like it, but I'll take the brunt of that". Annika won 72 times, and Charlotta won once - at the 2000 Standard Register Ping in Arizona.
Lurking in fourth place, one shot behind Kirk, are recent major champions In-Kyung Kim and Sung Hyun Park, along with former world No.1 Lydia Ko who is coming off a second-place finish to Lexi Thompson in Indianapolis last week.
Moriya is now ranked 32nd in the world.
Song shot a bogey-free 5-under 65 on Saturday and sits four strokes behind leader Moriya Jutanugarn heading into tomorrow's final round of The Evian Championship. "I mean, like I said at the press conference afterwards, because my goal was - I didn't set any goals going to the U.S. Open, and I would think maybe top 10 would be a great result for me, and I actually ended up having a top 5, so nothing to complain".
At 35, Kirk's first win in seven years in Wisconsin in July has rekindled her appetite for the game.
Park had been six over through just five holes in the rain and wind before play was abandoned and all scores wiped.