Gardaí want each district headquarters to have its own Facebook page, which would allow local officers to respond more quickly to complaints.
Rank-and-file gardaí said there has been a significant increase in the number of social media complaints reported to them locally, mainly concerning bullying and sexual harassment.
Officers in regular units say anything up to 20pc of cases referred to them involve some element of social media.
But they feel restricted in their investigations into the complaints because of a lack of access to the internet.
At the moment, gardaí either have to use their own Facebook account, which they are reluctant to do because it contains private family content, or else apply for permission to Garda headquarters to be given access for a specific inquiry.
The other option is to contact the relevant specialist unit and ask its members to check out the internet content for them.
Ray Wims, who is a central executive member of the Garda Representative Association, wants each district headquarters to have its own website, which would allow local gardaí to respond more quickly.
"We should embrace social media and use it to our own advantage, not only for inquiries into complaints from the public but also to respond to false accusations against us and also to publicise the good work we carry out in the community," Mr Wims said.
"The PSNI has local websites for district officers and it works very successfully."
However, a senior Garda officer said they had specialists such as the cyber crime and computer crime units, who were trained and skilled in how to investigate online content.
"It does not make sense to appoint one officer in each district headquarters to spend the day monitoring social content when we have special units with the proper skills to perform those duties anyway as well as the know-how on how to best progress those inquiries," he said.
Gardaí say they are working with online service providers to respond more rapidly to complaints about social media.
Providers such as Facebook are coming under pressure to act more quickly in withdrawing objectionable or inappropriate content. Gardaí have lines of communication open to the providers but officers admit the lengthy response time can be frustrating.
In a statement to the Irish Independent, Facebook said it works within the SPOC (single point of contact) system which makes communication with police forces straightforward and fast. It added: "As a responsible company we work with law enforcement where appropriate and to the extent required by law to ensure the safety of the people who use Facebook."
Standing in front of me are a concerned mother and father accompanied by their teenage daughter. Just days earlier the minor had sent sexually explicit pictures of herself to her underage boyfriend.