Moore, 50, who got along with the 26-year-old art dealer at supermodel Naomi Campbell's boyfriend's 50th birthday party in India, is dating him a year after splitting from her younger husband Ashton Kutcher.
"They were dancing and grinding all over each other, openly, in front of other guests. Since then they have been quietly spending time together," a source said.
Schnabel had dated an older woman earlier. He went out with Australian supermodel Elle Macpherson when she was 44 and he was 21 and has been linked with "Lord of the Rings" beauty Liv Tyler, 35.
Moore split from "Two And A Half Men" star Kutcher, 34, after he had a one-night stand on their sixth wedding anniversary.