A bill will be introduced to the Dáil later that would cap the amount of a media outlets that one person can own.
The Social Democrats bill would also be retrospective - meaning it could force anyone who owns over 20% of a media company to sell some of their interests.
The Social Democrats say it is about principle and is not out to target businessman Denis O'Brien.
TD Catherine Murphy says the bill would help to secure the plurality of the press: "I think it's really important that we have a media that there is a great degree of plurality, that it is open and independent and that it is robust.
"We have plenty of examples, for example after the economic crash it was concluded that there was a great deal of group think, so I think that just shows you that it is important that we have a media that is diverse."