Months after finalising her divorce from Johnny Depp, Amber Heard is reportedly ready to "settle down and have a family" with her new billionaire beau.

The 30-year-old actress has been romantically linked to Tesla boss Elon Musk, with her father saying she is "serious" about her new relationship.

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"Amber and Elon are both very serious about each other. She would love to get married," Heard's father, David, told Grazia magazine, according to MailOnline.

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"One of the things they want to do is settle down and have a family. They are making plans for that."

However, a source close to Musk has refuted the reports, saying that "they have no plans to get married. Moreover, Amber is currently in Australia shooting the Aquaman movie for the next six months."

Amber Heard with her now ex-husband Johnny Depp. Photo / AP
Amber Heard with her now ex-husband Johnny Depp. Photo / AP

Heard was first linked to Musk, 45, in the middle of last year, after the pair were spotted together in London and Miami.

The pair attended a screening of Al Gore's An Inconvenient Sequel: Truth to Power in California last month, The New York Post reported.

Sources told The Hollywood Reporter in August last year that Musk "became" infatuated with Heard after they appeared in the 2013 film Machete Kills.

Musk, who is worth an eye-watering $US13.9 billion ($18.3 billion), is the mastermind behind the ultra high-speed Hyperloop transport system, and also founded rocket manufacturer SpaceX with the aim of colonising Mars.

The dad-of-five has been married three times - twice to British actress Talulah Riley, however she filed for their second divorce in March last year, the Sun reports.

Heard filed for divorce from Depp, 53, in May last year, amid allegations he physically and verbally abused her - claims he has repeatedly denied. The divorce was finalised in January.