The couple, who have been dogged by break-up rumors for the past month, are said to be living separately.
"My sense is that this is a couple which hasn't existed for two years," a source told People.
Another insider claimed that the two's move to Los Angeles was to blame for the split. They previously lived in France.
"They bet that they could move to California and be on long stays on film locations for his career. They bet that things would continue there as they had in the south of France. They lost that bet," the insider told the magazine.
"Vanessa went seven years between albums and several years between film projects while he became Captain Jack Sparrow."
Angelina Jolie has reportedly been working with the couple in an attempt to save their relationship.
Listen to Johnny Depp and Vanessa Paradis cover 'Ballade De Melody Nelson' below: