The pair dined out at the South Beverly Grill, reports E!, and have spent several nights at Moore's home.
"They have been trying to keep it a secret," a source told E! "It's not a serious thing...but it may develop into something. They have a lot of fun together and have been meeting in secret places in New York and Los Angeles."
Morton, 31, famously dated Lindsay Lohan in 2006 where he often hung around the set of her stinker of a movie, Georgia Rule.
Demi, 50, is in the process of divorcing Kutcher, who she publicly dumped amid a cheating scandal 14 months ago.