Johnny Depp has reportedly stormed off the Australian set of "Pirates of the Caribbean: Dead Men Tell No Tales" to return to the United States to be with wife Amber Heard.

The superstar actor is meant to be shooting scenes as swashbuckling Captain Jack Sparrow on the Gold Coast tourist strip in Queensland state, but walked away on Wednesday evening, the Gold Coast Bulletin said.

"He’s going back to the States on the first available private charter flight he can get on,” it cited a source on the production team as saying.

The newspaper said Depp and his wife of three months were constantly bickering with some US entertainment websites claiming she had previously been asked to leave the set because their arguing was causing disruptions.

Heard is believed to have returned to the United States with the couple's two dogs Boo and Pistol last week, which were forced out of the country after officials warned they would be destroyed because they had entered the country without authorisation.

The couple bought the terriers into Australia on their private jet without going through quarantine procedures, with Agriculture Minister Barnaby Joyce telling them to "bugger off" back to Hollywood, sparking a social media frenzy.

The Bulletin said Deep had initially been scheduled to return with them but changed his plans at the 11th hour after the film’s producers intervened.

If he does leave, it will be another major setback for the Disney movie, which is already behind schedule after he suffered a hand injury and returned to the United States to recover in March.

The Bulletin said representatives for the producers, Disney Pictures and Jerry Bruckheimer Films, were desperately trying to convince him to stay.