A Fine Gael TD wants to make it an offence to comment on ongoing criminal trials.
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, a jury cleared TD Paul Murphy and five other men of the false imprisonment of former Tánaiste Joan Burton and her advisor during an anti-water charge demonstration in Jobstown in 2014.
Ms Madigan admits we do not know if social media had an influence on the jurors, but she said we need legislation to protect juries from outside influences.
The TD is now going to try and bring a bill to the Dáil making it a statutory offence to comment on ongoing criminal cases.