A Fine Gael TD wants to make it an offence to comment on ongoing criminal cases.
It follows the use of social media during the Jobstown trial.
Josepha Madigan - a Fine Gael TD and solicitor - believes our laws need to be updated to cover the increased use of social media
In an interview with the Sunday Times she said she found some comments made by Solidarity TDs during the Jobstown trial as very menacing and she believed there had been an attempt to influence the jury.
On Thursday jurors cleared TD Paul Murphy and five other men of the false imprisonment of former Tanaiste Joan Burton and her advisor during an anti water charge demonstration in Jobstown in 2014.
Ms Madigan admitted we don't know if social media had an influence on the jurors but she said we needed legislation to protect juries from outside influences.
The TD is now going to try and bring a bill to the Dail making it a statutory offence to comment on ongoing criminal cases.