The city council is requesting approval to convert a student accommodation block on Smithdown Lane east of the city centre into apartments for homeless people.
The five-storey Smithdown Court can accommodate 59 people and would replace the authority’s former Rough Sleeping Night Hub, Labre House, on Camden Street.
Labre House, which has dormitory-style sleeping arrangements, was closed during the pandemic to curb the spread of Covid-19.
Those using the facility were relocated to more suitable alternative accommodation in the short term but the council has now confirmed that Labre House will not reopen after the pandemic.
As a result, a facility with self-contained bedrooms is required to make up for the shortfall of bed spaces.
Around £2m is earmarked to acquire and convert Smithdown Court, subject to planning approval.
The funds are part of the £6m the city council was awarded by the Government to support projects aimed at providing shelter for homeless people.
The rooms would be available to individuals for up to six months, according to a council report.
Should planning permission be granted, work to convert the building would not start until the end of the current tenancy agreements, which expire at the end of June.