Justice Secretary Shabana Mahmood is said to be considering the plan, which was drawn up by her Tory predecessor Alex Chalk.
It comes nearly a year after Ms Mahmood derided the proposal as "no greater symbol" of the state of the criminal justice system.
Meanwhile Labour minister Angela Eagle did not deny that the Ministry of Justice was considering a deal with Estonia when she spoke to reporters yesterday.
At the same time, Britain's prison population reached another high, with 88,521 people behind bars 171 more than the previous record set at the end of last week. The rise is likely to be driven by court cases following recent riots.
Next Tuesday Labour's temporary early-release scheme starts, where some prisoners will be freed after serving 40% of their sentences.
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