UK ministers remain committed to building a new prison in Wales, according to the justice secretary.
Robert Buckland said he was hoping to work with local councils and the Welsh Government "to make sure that can become a reality".
Plans for a new "super-prison" in Port Talbot were withdrawn after strong local objections.
Mr Buckland said he was also "very interested" in developing a women's centre in Wales.
The five prisons currently in Wales - HMP Berwyn, HMP Cardiff, HMP Parc, HMP Swansea, and HMP Usk/Prescoed - are all for men.
Speaking to the BBC's Politics Wales programme, Mr Buckland accepted there was a "problem" with female prisoners from Wales having to serve sentences in England but said he had to balance the idea of a women's centre "against all the other competing priorities".
Last summer, Boris Johnson announced plans to create 10,000 new prison places in Wales and England.
Mr Buckland, the second Llanelli-born Lord Chancellor after Lord Elwyn Jones (1974-1979), said he "would love" an extra Welsh prison to be part of the programme.
A new category C super-prison for up to 1,600 prisoners was planned for Port Talbot before UK ministers withdrew the plan after strong local opposition.
Asked if the UK Government still had plans for a similarly-sized facility, Mr Buckland said: "We still want to build an extra prison in Wales.
"I'm not so much interested in the glib titles, I want to make sure that we have a facility that is the right size and the right model, and that actually delivers purposeful prison activity.
"I'm not going to commit myself to a particular size prison now.
"What I do commit to is a real concern about the fact that I think having an extra prison in Wales would be good for the local population.
"I've got to get on with that apace. I want to deliver it by the middle of the decade, so my officials will do whatever they can to identify sites in England and Wales that fit the bill, and that can deliver those extra places," he added.
Research published by Cardiff University's Wales Governance Centre in January 2019 claimed Wales has the highest imprisonment rate in western Europe.
Mr Buckland also signalled opposition to transferring full control of the justice system in Wales to the Welsh Government.
A commission chaired by Lord Thomas of Cwmgiedd called for the devolution of policing and prisons because people in Wales are "let down by the system in its current state".
Mr Buckland, the Conservative MP for South Swindon, said: "I think the question you've got to ask yourself is 'what is the outcome?'
"It's all very well obsessing about process, working out which desk is going to be responsible for what.
"What is more important I think from the point of view of residents is outcomes."
"Making our streets in Wales safer, I find that's what the public would expect me and the home secretary and the prime minister to be concentrating on, rather than worrying about who holds the pen," he added.
A Plaid Cymru debate called for the devolution of criminal justice at the Senedd on Wednesday.
"For a fraction of the amount that we are spending keeping people in prison we could invest in a really good quality probation service," said Leanne Wood, Plaid AM for Rhondda, in an interview on BBC Radio Wales' Sunday Supplement.
"These are the things that we need to tackle," said Ms Wood.
"They are not being tackled at the moment and we could tackle them if devolution of criminal justice was seen through."
After Friday's inquest, the National Probation Service in Wales said it had taken responsibility for managing all offenders on licence in Wales from the Community Rehabilitation Company.