The 23-year-old Australian was again in red-hot form as she shot a flawless second-round of seven-under 65 on Friday to be tied fourth at the halfway point in the Portland Classic.
Backing up her opening 66, Kim was at 13 under and three shots behind Dutch leader Dewi Weber, who had a 62 to be two shots clear of 2022 winner Andrea Lee (63) and Germany's Polly Mack (67).
Kim gave herself a chance to make Australia's Olympic team when she surged up the world rankings by winning the Lotte Championship in Hawaii last December, admitting it was on her mind.
But it was always going to be a longshot to get past major winners Hannah Green and Minjee Lee who made it to the Paris Games for next week's women's event as the two best-ranked Aussies.
In only her second season on the LPGA Tour, Kim has plenty of time to play in future Olympics.
The Games are much on the mind of leader Weber, who is out to prove a point after being denied a spot in Paris because the Dutch Olympic committee didn't think she was good enough to contend.
Weber qualified for the Olympics under International Golf Federation standards, but was left out because of the country's separate standards for all sports to meet a realistic chance of a top-eight finish.
"We're two rounds in, so we'll see how this all unfolds and if I can really make a statement," said Weber, after reeling off 10 birdies in her 10-under 62 on Friday, including nine in an 11-hole stretch.
"Of course it's in the back of my mind because it's the week before the Olympics. It was something that I was looking forward to. ...
"It sucks, but all we can do is like try to prove why those standards were so silly, and I really hope to do that on Sunday."
Playing only her second LPGA Tour event of the year, 28-year-old Weber is now in hot pursuit of a first LPGA title.
"I did a really good job both days of just going shot for shot, which I know is such a cliche but I've never been able to really do that," said Weber, who has four top-seven finishes in 11 starts this year on the secondary Epson Tour.
Kim was tied fourth with Jenny Shin (65) with Americans Alexa Pano (64) and Emma Talley (67) another stroke back.
Robyn Choi was next-best Australian, tied 13th at 10 under after a 67 with Gabriela Ruffels (69) two shots further back and Hira Naveed (70) at seven under, while Sarah-Jane Smith (four under), Su Oh (two under) and Sarah Kemp (two over) missed the cut.
With the Olympics next week, no one from the top 30 in the world ranking is in the field. The lone Olympian in the field is Aditi Ashok of India. She was seven under after a 67.
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