The group is consulting with 33 staff on plans to close its printing site near Cardiff Docks.
Trinity Mirror wants to print the Western Mail in Watford and the South Wales Echo in Oxford, it is understood.
The company said the consultation process was ongoing.
The group previously blamed "declining print volumes and the relocation of a number of titles within our print network" for the proposed closure of the print works, which is responsible for a number of Trinity Mirror newspapers as well as other publications.
Trinity Mirror also owns Wales on Sunday, which is already printed in Birmingham, as well as the South Wales Evening Post and the Daily Post.
Meanwhile, BBC Wales understands the company is in talks to sell its Media Wales building in Cardiff city centre.
The company plans to remain as a tenant when the deal is completed.
Media Wales moved into the six storey purpose-built office block on Park Street in 2008.
Staff cuts mean its sales and editorial teams now only occupy one floor, while accountancy firm Deloitte has taken some of the vacant space.
Trinity Mirror declined to comment on the proposed sale of its Media Wales headquarters.

The Change Britain campaign is being led by Mr Johnson's former Vote Leave colleague, Labour's Gisela Stuart.
The group's main aim is to ensure that PM Theresa May's delivers on her promise that "Brexit means Brexit".
Mr Johnson said the group would make sure that the UK gained control over "laws, borders, money and trade".
His comments came as former cabinet minister John Whittingdale urged Mrs May to speed up the formal process of breaking away from Brussels, rather than waiting until next year to trigger Article 50 - after which both the UK and EU will have two years to negotiate the terms of the split, with any extension having to be agreed by all 28 EU members.
In a recorded a video message, in which he declared his support for the campaign, Mr Johnson said: "On June 23 the people of this country voted to leave the European Union and they voted for change.
"They did so by a clear majority. But there were many people who also voted for Remain.
"So it's absolutely vital that we work together, Leavers and Remainers, as we seize the opportunities that this country now has to forge a positive and exciting new relationship, not just with the European Union, but also with the rest of the world; changing Britain and making it global again.
"Now more than ever we need to show the British people that, as politicians, we are listening to what they have to say.
"Brexit means Brexit and that means delivering on their instructions and restoring UK control over our laws, borders, money and trade."
Ms Stuart said the EU referendum meant the country would undergo "the biggest change in 40 years in our diplomatic, trade and economic relationships".
"It also creates a unique opportunity to review our democratic and constitutional arrangements," she said.
"The referendum also marked a more profound political change than a change of occupancy in Downing Street. It has forced us to acknowledge that people in large sections of the UK have lost faith in political parties and the Westminster elite.
"While millions in this country enjoy unprecedented prosperity and freedoms, many millions more feel despair at their sense of exclusion and diminishing prospects."
Meanwhile, Mr Whittingdale, the former culture secretary, urged Mrs May to push ahead with triggering Article 50, which begins the formal two-year process of leaving the EU.
"Article 50 is the beginning of the process rather than the end," he told the Daily Telegraph. "We do need to get the formal process under way. I don't say that it has to happen tomorrow but I would like it to happen pretty soon, and by that I mean weeks, not months."
And Labour leadership hopeful Owen Smith said he would consider applying to rejoin the EU if he became prime minister after UK had already left.

18 February 2016 Last updated at 11:41 GMT
The black saloon car hit the man at about 18:50 GMT as he crossed Copyground Lane on 9 February.
Police have appealed for the driver and witnesses who came to help the victim, to come forward
The man was taken to hospital for treatment and has since been discharged.
Newspaper publisher Trinity Mirror plans to print some of its Welsh titles in London and Oxford when it closes its presses in Cardiff, BBC Wales has learned.
[NEXT_CONCEPT]
Foreign Secretary Boris Johnson has thrown his support behind a new cross-party campaign aimed at ensuring the UK leaves the European Union.
[NEXT_CONCEPT]
A 50-year-old man was left with knee injuries after a car hit him in High Wycombe before driving off.