Interesting, Moore dated Harry for about six months before they amicably parted ways in May, reported E! Online.
Moore was spotted on a dinner date with Morton recently.
"They are into one another. Morton is very charismatic and she loves that about him. He's a go-getter," a source said.
Meanwhile, Moore, 50, is very grounded and the 66-year-old is "learning from her spirituality."
The twice-divorced restaurateur, the son of famed steakhouse founder Arnie Morton, co-founded the global Hard Rock Cafe chain in 1982.