The owners of St Kilda's controversial Gatwick Private Hotel have received several offers to buy the property, raising expectations a multimillion-dollar sale will soon proceed.

Agents for the notorious Fitzroy Street boarding house believe the sale could be completed possibly within a week.

The Gatwick has been advertised at $11 million to $12 million and is expected to reach that range.

Lemon Baxter associate director Richard Hutton said the owners were considering several offers for the property. About 40 groups, local and international, had inspected the building, Mr Hutton said.

"The level of interest has been very high," he said. "A lot of them are aware of the building and its history and they are keen to secure a presence in that area."

Mr Hutton said the sale contract would include a 12-month settlement to allow the residents to relocate.

The Gatwick is owned by sisters Yvette Kelly and Rose Banks, who have worked at the boarding house for decades. Some of the residents have lived there for years, while others stay for short stints.

Violent outbreaks, stabbings and even murders have occurred at the Gatwick.

It has dozens of rooms and is a reminder of the many large, old-style rooming houses that were once common in St Kilda.

In December, Ms Kelly said Melbourne's ice scourge and building maintenance costs had prompted the sisters to put the Gatwick up for sale.

She said it was not the tenants causing problems but "people coming in".

Housing Minister and local MP Martin Foley said the Gatwick had been part of St Kilda's "diverse social fabric" for more than 50 years.

"It provides a refuge of last resort for many vulnerable people, sadly in conditions that no longer meet contemporary expectations," he said.

But Mr Foley said the state government had no role in the sale beyond undertaking to look after the interests of long-term residents to ensure they were "suitably housed".

West St Kilda Residents Association president Colin Fryer said supported accommodation would be a better option for Gatwick residents with nowhere else to go.

"The majority of people acknowledge it's been a refuge, a last port of call for people who can't find anywhere else to put their head down," he said.

Mr Fryer said there had been an increase recently in people sleeping rough in St Kilda. That observation is consistent with a recent count of rough sleeping by the City of Melbourne, which also reported a substantial rise.