The 51-year-old actress sparked romance rumours after she was spotted getting cosy with Friday, 27, on a beach in Mexico during the festive season, reported Us magazine.
"Rumer brought (Demi) to a show in Los Angeles. She thought he was a fun guy her mom would like," a source said.
The couple, who are currently enjoying each other's company are reportedly not serious yet.
Moore, who finalised her divorce from Ashton Kutcher in November l last year, got separated from the 'Jobs' star in 2011 after six years of marriage.