Both brothel buildings are on the market with the Daily Planet tipped to fetch about $5.5 million, and the Playhouse, located in a far less salubrious industrial estate in Melbourne's west, about $1 million.

The Daily Planet is owned by Australia's only ASX-listed strip club and brothel owner Planet Platinum, which was tipped into administration last year after the Australian Securities and Investments Commission alleged a string of serious governance breaches against its founder John Trimble, the nephew of notorious underworld figure Robert Trimbole​.

Platinum's liquidator John Lindholm recently sold off another of its assets, the sleaze and violence-prone CBD strip club Showgirls Bar 20 on King Street.

It was snapped up for $13.25 million by Lorenz Grollo who is midway through transforming the foyer of Rialto Towers – half owned by the Grollos – on the corner of King and Collins streets into an upmarket retail centre.

Mr Trimble's Daily Planet has had its own battles with authorities.

Local council officers discovered in 2005 Mr Trimble had knocked an illegal doorway into the neighbouring building at 13 Horne Street, which he also owns, and set up beds for 20 prostitutes without meeting any mandatory safety requirements or planning approvals.

That building will be also auctioned on the same day in November by Gross Waddell, as will another next door at 15 Horne Street.

Selling three buildings in a row is expected to tempt significant developer interest, particularly given Elsternwick's hip inner-city reputation.

Gross Waddell agent Alex Ham said the illegal doorway between the Daily Planet and the neighbouring building remained.

"The brothel will still be operating until auction day," Mr Ham said. "There is an agreement in place where either the purchaser or John Trimble can terminate the lease within 30 days."

Whispers in Hoppers Crossing, which has suffered far less controversy, has been put up for a mortgagee sale by Bendigo Bank through agents Sutherland Farrelly.

It's a purpose-built brothel in the backblocks of an industrial estate that has a reception, waiting rooms, six bedrooms with ensuites and a self-contained manager's residence, all of which bring in $130,000 rent.