In a cover story for this week's issue of People called "Love Gone Wrong", the celebrity magazine quoted several unnamed sources as saying the pair's relationship is nearing an end.
The "Pirates of the Caribbean" star, 48, and Paradis, 39, never married but have been together since 1998 and have two children. They divide their time between France and the United States.
People magazine noted that the pair have not appeared on the red carpet together for more than a year, missing both the Cannes film festival in May 2011 and the Golden Globe Awards in Beverly Hills on Sunday, where Depp was a presenter.
"According to multiple sources....(they) are all but officially finished," People said.
Depp's representatives did not return calls for comment on the People story, which hits newsstands on Friday.
(Reporting By Jill Serjeant; Editing by Bob Tourtellotte)
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