The Rum Diary co-stars reportedly became engaged over the Christmas holidays (Dec13) and the 27-year-old beauty fueled the claims last month (Jan14) after she was photographed with a large diamond ring on her wedding finger as she cheered on Depp at a gig in California.
However, it appears Heard is not yet ready to open up about the relationship - she hung up the phone when an interviewer from the New York Daily News attempted to broach the subject at the end of a chat about her new Kevin Costner movie, 3 Days to Kill.
Describing the incident, the writer explains: "Suddenly, Heard said, 'You know what? I have to end the interview now,' and then she did."
But the famously-private couple has not shied away from public appearances together - Depp accompanied his new love to the Hollywood premiere of 3 Days to Kill on Wednesday night (12Feb14) and they posed for photos together on the red carpet.
The 50-year-old actor began dating Heard in the summer of 2012 following the breakdown of his 14-year relationship with French singer/actress Vanessa Paradis, the mother of his two children.