A government minister has refused to deny reports that officials are looking at sending criminals convicted in England and Wales to Estonia to serve their prison sentences.

The Daily Telegraph reported that the Ministry of Justice was investigating “all viable options” to increase capacity after the Baltic state said it had offered to rent out spare capacity to other countries.

Citing government sources, the Telegraph said the solution was “on the table” after men’s prisons in England and Wales almost ran out of cells last month with 83 spare spaces.

Angela Eagle, a minister in the Home Office, did not comment directly when asked on Sky News whether the government was considering renting cells for British prisoners in Estonia as it was “not directly my ministerial responsibility”.

She said: “I’m sure that colleagues are considering all sorts of actions to deal with the crisis that we’ve been left by the previous government in prison places and the prison service, and the criminal justice system generally.”

She added: “The last government closed loads of prison places and didn’t replace any of them, so I think that colleagues in the MoJ will be considering anything that they can to alleviate the problem.

“What we cannot have is people who are convicted of perhaps violent or serious crimes not being able to be in jail.”

The Telegraph reported that Estonia’s low crime rate had left its prisons half empty, prompting hopes that criminals convicted in England and Wales could deliver a €30m (£25m) boost to the country’s public finances.

The justice secretary, Shabana Mahmood, and Liisa Pakosta, her Estonian counterpart, were expected to discuss prison leasing on the sidelines of a Council of Europe event in Vilnius, Lithuania, on Thursday.

Pakosta told the Telegraph: “The UK and Estonia have a history of successful international co-operation, and such a partnership would create further opportunities to benefit and learn from each other.”

Sending offenders to Estonia was first proposed by Alex Chalk, the former justice secretary, at last year’s Tory conference. Labour criticised the idea at at the time as an example of Tory incompetence and underinvestment, while the Prison Reform Trust called it “half-baked”.

The number of people in prison in England and Wales has risen from about 40,000 in 1991 to more than 88,000 today.

Next week, about 1,500 people are released from prison under an emergency measure that reduces from 50% to 40% the proportion of custodial sentences to be served in prison for some.

The SDS40 scheme, which will free 5,500 prisoners over two months, will be launched on 10 September for those serving sentences of five years or less. A second category of prisoners – those who have served sentences of five years or more – will be released on 22 October.