|Moore with ex husband Ashton Kutcher|
The pair first got together earlier this month at Naomi Campbell's 50th birthday party for her boyfriend Vladimir Doronin in Jodhpur, India, and sources say they couldn't keep their hands off each other.
One told the New York Post newspaper: "They were dancing and grinding all over each other, openly, in front of other guests."
Since the party, the couple have been "quietly spending time together".
Vito has previously dated 49-year-old model Elle Macpherson and 35-year-old actress Liv Tyler, while Demi has three grown-up daughters with first husband Bruce Willis.
Demi announced her marriage to 'Two and a Half Men' star Ashton was over last November although the pair are yet to finalise their divorce.
Ashton is now dating actress Mila Kunis while Demi has been working on her health after being admitted to rehab earlier this year, where she was allegedly treated for eating disorder issues, exhaustion and substance abuse.