Green signed for a second straight 2-under 70 to be 4-under through 36 holes and trailing leader Holly Clyburn by four shots.
The 22-year-old is sharing fifth place and is the leading Australian at the event, Rebecca Artis a shot further back and in a share of seventh position.
Just 17 players are in red figures at the tricky Bonville layout with the cut falling at 6-over-par after the opening two rounds.
Overnight leader Clyburn added a 3-under 69 to her opening 67 to be 8-under and two clear of France’s Celine Boutier and Germany’s Olivia Cowan.
Iceland’s Vladis Thora Jonsdottir is outright fourth at 5-under with Green and Denmark’s Nanna Koerstz Madsen sharing fifth at 4-under.
Clyburn was impressive on day two and looked to be running away with the tournament when she got to 4-under through 10 holes but things quickly went awry with three dropped shots in her next four holes.
The 2015 NSW Women’s Open winner looked to be coming back to the field but finished her round in style with birdies at each of the final two holes to once again put herself in a commanding position.
“I played fantastic on the front nine, and it could’ve been a lot better,” she said after her round.
“Then I had an awkward yardage on 11 that made the round go upside down a bit. I took a three-putt there.
“But other than that I ground it out, I played some really nice golf coming in.”
Green, who is reportedly feeling under the weather after a recent hectic schedule, had a more adventurous round with four bogeys offset by six birdies.
The rising West Australian star would be entitled to feel some fatigue after posting a T11 finish in her LPGA Tour debut in the Bahamas before a frantic trip home to tee up in the Vic Open where she finished third.
She backed up that performance with another third-place finish at last week’s Women’s Australian Open but hasn’t been quite as sharp this week.
“I don’t feel like I played my best golf,” she said after signing her card.
“I felt like I left a lot out there. I had four three-putts, and a lot more opportunities that I could’ve taken advantage of.”
The final two rounds of the tournament will be broadcast live on FOX Sports More, channel 507, from 1pm-4pm both Saturday and Sunday.
SIGNATURE HOLES - 16TH AT MONA VALE GC, SYDNEY:
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