The Government is believed to be considering legislation that would take unpaid water charges from people's income and welfare payments.
The latest figures reveal that 1.23 million people have registered with Irish Water.
The company feels there is a total of 1.5 million customers.
Minister for the Environment Alan Kelly didn't confirm or rule out the reports.
He said on RTÉ's Claire Byrne Live: "I'm not going to pour cold water on it for the simple reason that is this, from an equity and a fairness point of view, you know we've 66-67% of people who have signed up and that needs to be respected."
Earlier on Monday, Kelly said that legislation will be brought to deal with people who haven't paid their water charges.
Kelly respected anybody who was involved in the Irish Water protest at the weekend.
He said on RTE radio One: “The people are coming with us.
“If you have two people sitting side by side in a bus and one person is registered and the other person isn’t, they say they are not going to pay, I can assure you from a Government point of view that legislation regulations will be brought in to ensure that everyone will treated the same.
"And there will be enforcement, whereby anyone who refuses to pay that legislation will be there to deal with that.
“There will be a distinction between those who can’t pay or are finding it difficult to pay and those who just refuse to pay,” he said.