The 50-year-old actress, who was married to actor Ashton Kutcher, enjoyed a brief fling with Schnabel but the art dealer broke off their relationship after she flew to Miami to join him for Art Basel as he was worried that the attention would distract him from his career, reported Examiner online.
"Vito has worked very hard to be taken seriously in the art business and doesn't want to be seen as somebody who dates celebrities. He hated having photographers follow him around after work got out about him and Demi," a source said.
Meanwhile, Moore's daughters are very concerned about her recent behaviour, when she attended a party in Miami and began acting very oddly and dancing strangely.
Moore and Schnabel first met at the lavish birthday bash of supermodel's Naomi Campbell billionaire boyfriend Vladimir Doronin in India in November.