Fareham Borough Council’s executive leader Sean Woodward says the local authority has expressed an interest in acquiring Fareham Magistrates Court in Trinity Street.
The building shut its doors to the public for the final time at the end of last month.
Its closure has led to the borough council expressing an interest in utilising the site.
Under its proposals, the building, which was constructed in 1994, would be demolished and turned into a flat complex or homes.
Councillor Woodward said: ‘We know that the Ministry of Justice are looking to sell the site as it is now surplus to requirements.
‘Therefore, we have expressed an interest in acquiring the site as I believe it to be an ideal place for housing, as it is on a brownfield site and that means we’re not building on our green spaces.’
The borough council are currently identifying brownfield sites in the town to develop a new Local Plan.
Shaun Cunningham, Liberal Democrat councillor on the local authority said: ‘The magistrates court is an ideal site for housing.
‘As long as the scheme for it fits in with the nearby surroundings then it should be a great future for that location.’
‘Despite the building being a bit of an eyesore, we would not want a big tower.’
Richard Ryan, vice chair of Fareham Labour Party also supported the plans to purchase the site for housing.
He said: ‘The logical option for the site is to build housing on it.
‘Of course, it’s a great place to look to put affordable or social housing due to its location in the town centre.
‘It would suit a mix of both flats and homes.’
A spokeswoman for the Ministry of Justice that the court is marked for transfer to the Homes and Communities Agency meaning it is being earmarked for housing.
The court’s closure was confirmed by the HM Courts and Tribunal Service earlier this year.
A consultation launched last year found that Fareham’s court had no staff based permanently on the site.
It was used at approximately 43 per cent of its capacity during 2014/15.
All the court’s staff and services are at Portsmouth Magistrates Court.