The Department of Communications has written to Eir to see if the company's claim it could roll out the National Broadband Plan much cheaper "stacks up".
Eir says it could complete the project for €1 billion - around a third of the almost €3 billion price the Government intends to spend.
Under plans approved last month, a private consortium led by Granahan McCourt - the sole remaining bidder - would be appointed to roll out broadband to 540,000 homes and businesses in rural areas.
However, there has been widespread criticism of the planned spending by the State - with public spending officials warning it represents an "unprecedented risk".
Amid the concerns, Eir's CEO Carolan Lennon told a Dáil committee yesterday that her company could complete the NBP for "under €1 billion".
She stated: "It is clear to us that we can build rural fibre infrastructure at a lower cost than is currently envisioned in the plans."
She said the €1 billion cost would involve the same 'connection model' applied to Eir's previous work to connect 340,000 rural homes - but stressed it would be different to the NBP model currently envisioned by the Government.
Mrs Lennon expressed "real regret" that Eir had to withdraw from the NBP bidding process over commercial concerns and other issues - but insisted they entered the process "in good faith with one [aim] - to win it."
Opposition parties have called for the project to be reviewed and for the tender to go elsewhere if it's cheaper.
"We need to know if this offer is real"
Speaking in the Dáil earlier, Taoiseach Leo Varadkar said the Government first needs to establish if what Eir is saying is credible.
He said: "We need to know if this offer is real... we need to know if it stacks up... we need to know what kind of delay would be imposed on people in rural Ireland waiting for broadband if we went back to a new procurement process.
"I think everyone understands that you can't just give a company - a private or state company - a contract. There would have to be a new procurement process."
He added: "One of the things we want to find out, for example, is how there can be such a big difference.
"A concern that I have and a concern that the Department of Communications has is that a big part of that difference would be met by imposing higher charges on those 500,000 homes, farms and businesses in rural areas."
Fianna Fáil leader Micheál Martin, meanwhile, argued that it's time to halt the current process to look at alternatives.
Addressing the Taoiseach, he said: "You've been too dismissive so far of people who've raised legitimate questions about this issue.
"You've been too dismissive yesterday of the Eir submission - it deserves further analysis. I think alternatives should be considered."
He further suggested that the Government may have felt the need to announce the plan before the local elections.
Deputy Martin cited the concerns raised by Robert Watt, Secretary General of the Department of Public Expenditure and Reform - noting there is "cause for pausing and reviewing" the broadband plan.
