The management of the Sunday Tribune is considering outsourcing some commercial functions at the paper.
The company refused to comment yesterday, but sources at the paper said outsourcing was most likely to affect clerical and accounting functions.
It is not clear whether any advertising functions might be outsourced.
Sources said any job losses were likely to be extremely small.
Last year, Independent News and Media, which is a 29.9 per cent shareholder in the Sunday Tribune, outsourced a large number of functions.
The number of people working in administration in the Sunday Tribune is about 10, while the paper's advertising staff numbers are between 15 and 20.
A very small number of people work in accounts.
The Dublin Print Group of Unions is to seek a meeting with Sunday Tribune management if any outsourcing goes ahead.
SIPTU, the State's largest union, is likely to be centrally involved if outsourcing affects its members.
The Sunday Tribune has undergone considerable upheaval in the last two weeks with the departure of editor-in-chief and managing director Mr Jim Farrelly.
He has been replaced by Mr Michael Roche as managing director, while Ms Noreen Hegarty is to become editor.
Ms Hegarty is currently a senior editor at the Evening Herald.
The current editor, Mr Paddy Murray, becomes an associate editor.