Australians laid tributes of flowers and beer bottles at a statue of Shane Warne in Melbourne on Saturday, after the country woke to the shocking news the cricketing great had died from a suspected heart attack while on holiday in Thailand.

As many in the sporting world and beyond expressed grief, Australian Prime Minister Scott Morrison offered Warne's family a state funeral for the sportsman known to his compatriots simply as "Warnie."

"Shane was one of our greatest cricketers of all time ... but Shane was more than this to Australians. Shane was one of our nation's greatest characters," Morrison said in a statement.