The Pirates of the Caribbean star and the French singer/actress have been together since 1998 and share two children; Lily-Rose and Jack.
The pair has lived in Paradis' native France for several years, but speculation about a split mounted earlier this month (Jan12) amid rumours which suggest they have been living separate lives.
A representative for either party has yet to respond to requests for comment on the reports, but Paradis braved the press on Monday night to walk to the red carpet solo at the premiere of her new film Cafe de Flore.
Paradis quickly walked in front of the waiting reporters and photographers, stopping only briefly to pose with co-star Marin Gerrier and the film's director, Jean-Marc Vallee.
The couple last walked a red carpet together at the Cannes Film Festival in 2010 and Paradis was notably missing from Depp's premiere of The Run Diary in November (11).