Thai Police on Monday said autopsy results showed the 52-year-old had died from a suspected heart attack, confirming the death was due to natural causes with no signs of foul play.

Deputy director of Samui Hospital Songyot Chayaninporamet told reporters the autopsy showed Warne died of a "congenital disease".

Following his death on the Thai resort island of Koh Samui, Warne's body was taken by ferry to the mainland city of Surat Thani on Sunday.

It was transported to Thailand's capital, Bangkok, on Monday night with preparations underway for a return to Australia, according to multiple media reports.

An Australian government charter flight is being organised and Warne's body is expected to be transported to Melbourne on Wednesday or Thursday, the Nine Network reports.

Warne's family issued a statement on Monday night describing the night of his death on March 4 as the beginning of "a never-ending nightmare".

"Looking to a future without Shane is inconceivable," his father and mother, Keith and Brigitte said.

"Hopefully the mountain of happy memories we all have will help us cope with our ongoing grief."

Warne's son Jackson wrote: "To my brother, my best friend, to my Dad, I love you so much. I don't think anything is ever going to fill the void you have left in my heart."

Warne's youngest daughter Summer said she missed her dad "so much already" and wished she could have hugged him "tighter in what I didn't know were my final moments".

Eldest daughter Brooke said she loved him "to infinity and back" and would miss him forever.

"I am lucky and will forever be so proud to call you my Dad forever," she wrote.

Victorian Premier Daniel Andrews said Warne's family had accepted the government's offer of a state funeral.

"It will be an opportunity for Victorians to pay tribute to his contribution to his sport, to our state and the country," Mr Andrews said on Sunday.

Australian Associated Press