The 51-year-old actor's publicist said the story was not true and he was planning to jet back to America for his daughter Lily James's 16th birthday next week, reported Daily Mirror.
"I can't go into detail on our filming schedules or the movements of individuals but I can tell you that nothing in that report has any relation to reality," Depp's rep Michael Singer said.
"Mr Depp has been filming on schedule. It's business as usual with all participants working," he added.