The Daily Mail reports Wass claims Depp made "vulgar" comments while on the flight, including screaming that Heard "liked getting f****d on set" and accused her of the affair with Franco.
According to the publication, Depp claimed Heard had expressed Franco was "creepy and rapey" when she starred alongside him in the Pineapple Express.
Depp denied assaulting Heard or being out of control on the plane, and claims he warned her about Franco's advances.
"I may have done things that I have no memory of," Depp said. But he insisted "I am certainly not a violent person, especially with women".
In the first day of court proceedings, Depp's legal team made explosive claims that Heard had had affairs with Elon Musk and James Franco, news.com.au reports.
Both Musk and Franco have denied any romantic involvement with Heard during her marriage with Depp.
'Creepy' sketch
A courtroom sketch depicting Depp in court has been mocked online, Page Six reports.
Twitter users have criticised the sketch for not quite looking like Depp's usual tall dark and handsome appearance.
The ruthless comments included one which said: "The courtroom sketch of Johnny Depp looks like me at a funeral."
"If looked like Johnny Depp I'd be livid at this drawing," a Twitter user wrote.
"There's really no excuse for this," claimed another, noting the sketch didn't look much like Depp at all in their opinion.
"I know court artists have to leave the room and draw these things from memory, so they often don't render a great likeness."
Depp is suing the Sun's executive editor and publishers for an April 2018 article which claimed he was physically abusive towards Heard.
Executive editor of the Sun, 37-year-old Dan Wootton, was born in New Zealand and worked as a reporter for TVNZ's Good Morning before moving to the United Kingdom.
The case is expected to last three weeks.
- Additional reporting AP.
