The couple, who have dating each-other only for a few months, are said to be serious about each other and want to take the relationship to the next level, reported Sun Online.
"Chloe and Marc have totally fallen for one another. She's been looking into getting a place in New York, where they love to hang out, or Miami, where his family are based.
"Chloe doesn't always have great self-esteem and Marc is a mature and grounded father of five. He's old-fashioned and they seem to think he'll take care of Chloe," said a source.
Anthony was previously married to Jennifer Lopez and has two kids with her.