Humphries died on Saturday at St Vincent's Hospital in Sydney following complications from hip surgery stemming from a fall earlier this year.
He was 89.
Creative Industries Minister Steve Dimopoulos says talks are under way with the entertainer's loved ones about the best ways to honour his legacy.
A range of options are on the table including a state funeral.
"The primary mover of these things is the family because it's their gift effectively to decide in conversation with government," Mr Dimopoulos said on Sunday.
"So, yes, it could be that (a state funeral). It could be many other things."
Premier Daniel Andrews said Humphries would live on through his iconic writing and larger-than-life characters, particularly Dame Edna Everage who put the Melbourne suburb of Moonee Ponds on the map.
"But at the end of the day, he was a boy from Kew with big dreams. And he achieved them," he posted on Twitter.
NSW counterpart Chris Minns says Humphries popularised Australian larrikinism on the world stage but he doesn't want to "front run" any potential Sydney-based gesture or ceremony.
"(He was) an Australian legend and someone we'd love to honour," he said.
The Melbourne International Comedy Festival has also joined the chorus of local tributes to the revered comic despite its chequered history with the late star.
Humphries delighted and outraged audiences for more than half a century and was a founding patron of the festival, leading to it naming its annual prize for most outstanding act after him in 2000.
But an outcry over a series of comments widely seen as transphobic prompted the festival to rename its top gong in 2019.
The MICF said on Sunday it was saddened to hear of Humphries' passing and hailed his contribution to the festival during its formative years.
"Having started his career in Melbourne, Barry's early support, along with Peter Cook, helped kick off and raise the profile of the festival nationally and internationally," it said.
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