The Melbourne pub, named for wartime Labor prime minister John Curtin, is one of the oldest in Australia and was a popular watering hole for Bob Hawke.
The pub's managers posted on facebook that the building's owners have decided to sell - "making way, most likely, for apartments."
Mr Andrews said that while the pub's future was a private commercial matter, Victorians would like to see the pub saved, given its history.
"I'm sure the union movement and people who have enjoyed that first class establishment will get around it, and maybe [the owners] can revisit the decision they have made," he said.
Trades Hall Secretary Luke Hilakari said about $6 million would be needed to buy the venue.
"I'd like to get a very large hat and pass it around some of the comrades and unions and see if we can save this pub," he told ABC radio.
"We need these great indoor spaces in Melbourne, it's part of the character of this city, you've got these old pubs that are over 150 years old," he said.
"This is something we can't just let go, former prime ministers came through that joint... it is a darling of the left, so many union officials have been there."
He confirmed Trades Hall does not have the money to buy the pub, but said he was meeting with union secretaries with a view to a rescue plan.
The pub's managers said while they have a lease until November, they did not know what the future of the site might be.
"We have no idea what the developers will have planned for us," they said.
In 2016, developers illegally demolished another historic Melbourne pub, the Corkman Hotel.
They were fined more than $1 million and jailed after failing to turn the site into a public park.
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