Every household could get a "carbon cheque" to compensate for a potential tax increase.
The Taoiseach says there are no plans to increase carbon tax this year - but changes could be made to the levy in 2020.
Leo Varadkar has said the Government's looking to make sure any revenue from the tax is given back to households through one of two schemes.
He explained: "You can give everyone a carbon cheque or dividend in the post - you can do that by individual, or by household.
"You get that upfront if you like - it's designed to compensate you for the cost of the carbon tax. Those who use a lot of carbon obviously don't benefit as much, and those who have low-carbon lifestyles benefit more."
He said the other model would be to use the money to increase welfare payments or tax credits.
The Government is now hoping to achieve an all-party consensus on which model to follow.
Responding to the Taoiseach's remarks, the Green Party says it has already put forward a proposal for a carbon dividend - adding that it supports the measure "as one of the fairest ways to deliver a transition to a low carbon economy".
Green Councillor Ciarán Cuffe explained: “The aim of the carbon dividend, or carbon cheque, is to change behaviour.
"By placing carbon taxes and giving back what is taken to households it provides direct incentives for people to move to low carbon heating, better insulate their homes, use public transport and, overall, create a smaller carbon footprint."
He added: “While the carbon dividend is a fairer way than a simple carbon tax, we still need to make sure that every community has low carbon alternatives in heating and transport available to them."