Johnny Depp's estranged wife Amber Heard has been 'spending a lot of time' with billionaire space pioneer Elon Musk as she navigates her way through a very public divorce.

The Rum Diary star, 30, has known Musk, 45, for several years but sources claim the amount of time the pair are spending together recently has increased.

Musk, who is worth a staggering $12.7 billion, is going through a separation of his own. His wife Tallulah, who he had married, divorced and remarried, filed for divorce from the billionaire in March.

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Heading for divorce: A report from UsWeekly claims that Depp (pictured left with Amber in January) would like to hurry up the divorce process as much as possible while Musk is being divorced by his wife Tallulah (pictured right together in 2013). They married, divorced then remarried

According to TMZ, a source claimed she has been seeing the entrepreneur behind those sleek, eco-friendly Telsa cars for weeks.

Last weekend Heard and her sister were at Elon's hotel bungalow in Miami. She has visited him at his Los Angeles office and he has visited her at his home. Two weeks ago they allegedly had a 'one-one dinner' at his LA home.

The source warned it should not be called 'dating' but that it cannot be ignored that they have been meeting privately a lot.

It is a trying time for Heard who is in the midst of a messy divorce from Depp. She filed papers in court in May claiming the 52-year-old actor had been 'verbally and physically abusive' for the 'entirety' of their relationship.

The following month, text messages reportedly exchanged between Heard and Depp's assistant emerged detailing alleged assault by the actor including that he had 'kicked her'.

Entertainment Tonight reported that a source claimed the messages were sent between Heard and a man alleged to be Depp's assistant, Stephen Deuters, and are from May 2014.

In one text supposedly sent from Heard regarding a man alleged to be Depp she writes: 'He's done this many times before. Tokyo, the island, London (remember that?!), and I always stay. Always believe he's going to get better... And then every 3 or so month [sic], I'm in the exact same position.'

The text exchange dates back to before the estranged couple was married.

According to UsWeekly Depp - who was spotted visiting Alcatraz in San Francisco on Wednesday - wants to hurry up the divorce process as much as possible and also wants to keep the details of their split out of the public eye.

The pair, who wed after a whirlwind romance, had no prenup and Depp, who is worth a reported $400million, will not reveal his finances until Heard agrees to keep them private.

In the city by the bay: Johnny Depp let his troubles blow away on a trip to windy Alcatraz off the coast of San Francisco on Wednesday. The actor, who is worth an estimated $400million, wants to hurry the divorce from Amber Heard as much as possible and has refused to make his finances public until his estranged wife agrees to keep them private

Meanwhile, Musk, who has been described as the Thomas Edison of our times, co-founded PayPal, SpaceX and Tesla Motors, which produces cars with an advanced auto-pilot feature.

SpaceX, a privately funded space transport services company, has managed to land four rockets from space back on Earth, one on land and three on sea, with the latest successful sea landing on May 28.

Musk, a South African-born Canadian-American, recently said that he expects to launch a manned mission to Mars in 2024, which would arrive in 2025.

One of Musk's most ambitious projects is Hyperloop - a proposed method of travel that would transport people at 745mph between distant locations using pods that are pushed through tubes by magnets.

It was unveiled by Musk in 2013, who said it could take passengers the 380 miles (610km) from LA to San Francisco in 30 minutes - half the time it takes a plane.

But his incredible success has not come easy.

First wife: Elon Musk with Justine. The pair were married for six years and have five sons together

Stepping out: Elon Musk was pictured with his then wife, Tallulah at a conference in Sun Valley, Idaho in July 2015

Family fun day: Elon Musk recruited his sons to help when did the ALS ice bucket challenge in 2014

He had a miserable childhood in South Africa and where he was bullied by classmates and subjected to some psychological torture by his father. His experiences there would lead him to leave and head to the United States where he met his first wife, Justine Wilson.

The entrepreneur and the Canadian author were married for six years before divorcing. They have five sons together - triplets and twins. Musk revealed in an interview that he didn't like his children's school so he started his own. Ad Astra, which is Latin meaning to the stars, is shrouded in secrecy. It is believed to have only 20 pupils, and has no known websites or application process.

According to author Ashlee Vance in Elon Musk: Tesla, SpaceX and the Quest for a Fantastic Future, the billionaire met the second Mrs Musk at the famous London nightclub Whisky Mist in 2008.

She was still a virgin at 22 and he told her he wanted to show her his rockets.

She later said:'I was skeptical, but he did actually show me rocket videos.'