DMG Media Ireland - the group representing the Irish Daily Mail, the Irish Mail on Sunday, Extra.ie and EVOKE.ie - is seeking 35 voluntary redundancies from its workforce of around 156 in a bid to deliver "significant" cost savings.
However, the company has warned that if the offer is under-subscribed, it will implement compulsory redundancies.
DMG Media says the redundancies are part of a process to adapt the business in a rapidly changing media environment, as newspaper sales continue to fall.
Staff were informed of the package today, and employees across all brands and channels will be eligible to apply for redundancy.
However, it is understood that most of the redundancies will target the Daily Mail rather than its weekend sister papers.
Staff made redundant will receive four weeks per year of service plus two weeks statutory capped at 25 years.
DMG Media Ireland Paul Henderson said the company would continue to ensure that the business was "future-proofed" and can adapt and grow through what he described as "undoubtedly a challenging time for newspaper publishing and the continuously changing media landscape".
Mr Henderson noted that the group's digital offering was continuing to grow, and now reaches over 3 million Irish adults per month.
He also said that a quarter of a million people buy their newspapers and magazines each week, adding that the company remained committed to developing their media portfolio to serve the demands of the future.
However, recent figures revealed that the papers' print circulation fell by almost 20% between July and December last year.
Just last January, Independent News & Media also announced it would be seeking 35 redundancies, mainly focused on the editorial element of its operation.
INM incorporates the Irish Independent, Sunday Independent, the Herald, Sunday World and Belfast Telegraph titles. It also has a 50 per cent holding in the Irish Daily Star.