A spokesperson for the Office of the Data Protection Commission has said the ODPC had "categorically" not been lobbied by former taoiseach Enda Kenny or his office.
It comes as the Government has been urged to provide clarification following claims in a British newspaper that Facebook lobbied leading politicians in several countries on its behalf.
The article in the Observer includes what it says are details of internal memos about Facebook's lobbying of politicians, including former taoiseach Enda Kenny.
The newspaper has published what it claims are leaks of documents, including an internal memo sent by the company's Chief Operating Officer, Sheryl Sandberg, following her attendance at the World Economic Forum in Davos in 2013.
It is alleged she raised concerns that the proposed European data protection legislation was considered a "critical" threat to the company and that it faced an "uphill battle" on the data and privacy front.
The report claims that the memo described a "great relationship" that Facebook had with the then taoiseach Enda Kenny and that because Ireland was about to assume the Presidency of the EU, there was an opportunity to influence the new data protection rules.
Mr Kenny did not respond to requests to comment on the report.
A spokesperson for the Irish Government said: "The Irish Government has a good relationship with all major investors in Ireland. The relationship with Facebook is no more nor less close than with any other large firm."
A statement from Facebook said that the leaks were "selective" and they "tell one side of the story and omit important context."
It said: "We regularly meet with Government stakeholders to explain how our services work and discuss topics relevant to our business."
Labour's Brendan Howlin said other EU member states depend on Ireland to be a "fair and impartial regulator of data".
He said the reports were "profoundly worrying" and that he was not made aware of any understanding between the Irish Government and Facebook when he was a member of that Government.
He said: "I read the rebuttal from Facebook saying that these were taken out of context, so there has to be a very full explanation of exactly what was understood by Facebook and what undertakings did Enda Kenny as Taoiseach give them."
Fianna Fáil’s James Lawless said an explanation on the matter was needed.
"We certainly need an explanation regarding this matter but we also need a tangible gesture of intent from Government that they are serious about appropriately dealing with the giants operating within social media," he said.