Lee is four shots off the pace in a tie for fourth after shooting a third-round four-under 68 on Saturday to be six under for the tournament.
Defending champion Green had a 67 to move 16 places up the leaderboard and five behind the leader.
World No.6 Green returned to women's golf's so-called "Major of Asia" with fond memories and plenty of confidence.
She notched birdies on the last three holes last year to snatch victory from Celine Boutier and become only the fifth Australian to win five times on the LPGA Tour.
Ko shot a 68 on Saturday to move from one stroke behind overnight to one stroke in front.
The 27-year-old New Zealander had a 54-hole total of 10-under 206 on the Tanjong course at Sentosa Golf Club.
England's Charley Hull, who birdied two of her first four holes, was a stroke behind in second after a 68.
Jeeno Thitikul had the best round of the day, a 66, to move into third place, three strokes behind Ko.
A Lim Kim, who led after the first two rounds, moved in the wrong direction with a 73 and was tied for fourth place with Lee and Thailand's Pajaree Anannarukarn (70).
Steph Kyriacou (70) was the next-best Australian, tied 51st at seven over, with Grace Kim (72) and Gabriela Ruffels (76) a further four shots back.
The Singapore field features nine of the top 10 players in the world ranking - and 13 of the top 15 - minus only top-ranked Nelly Korda and Rose Zhang.
The Singapore tournament is the second of three events on the LPGA's first Asian swing of the year. The final event will be played next week at Hainan Island, China.
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