Earlier this week, Portsmouth City Council confirmed it would give every household in the city five free lateral flow tests a month after April, in a scheme believed to be the first of its kind in the country.
It comes as the government brings an end to free lateral flow tests to members of the public, as of April 1.
Measures will still be in place for health and social care workers to obtain tests.
A spokeswoman for the county council said: 'Government-funded free testing for those with and without symptoms of the virus is due to finish at the end of this month.
'We will continue to closely monitor outbreaks, take necessary action as required and will await further national advice on the additional mechanisms for testing that may be available from April.
'This will enable us to continue protecting our most vulnerable populations within Hampshire, as the need arises.'
Portsmouth City Council's director of public health, Helen Atkinson, said the city's initiative would cost between £316,000 and £365,000, assuming a 10 per cent uptake from residents.
Under the new scheme, every household could claim up to five lateral flow tests per month, until June 30.
Hampshire County Council recently confirmed budget cuts of £80m, which will be made before April 2023.
The county council did not answer the question of whether such a scheme would be too expensive.