Simon Coveney said the list, which is set to be published on Monday, will not be particularly long and confirmed the United States would not feature on it.
People arriving in Ireland from overseas – with limited exceptions such as essential supply chain workers – are currently required to fill in a passenger locator form and self-quarantine for 14 days.
Those crossing the border from Northern Ireland are not subject to restrictions on their movement, however.
The introduction of the new green list will mean people arriving in Ireland from approved countries will be exempt from the quarantine rule.
Those arriving from countries not on the list will still be required to self-isolate for 14 days.
Commenting on the plan, Mr Coveney said Cabinet decisions on which countries would be included on the list will be based on science and epidemiological data.
He said countries will be excluded from the green list if their Covid-19 infection rates exceed a set threshold.
“I think there’s no question that the US will be on the green list, it won’t be,” Mr Coveney told the Pat Kenny Show on Newstalk.
Referring to the UK specifically, he added: “And I think it’s very unlikely our closest neighbour either will be under that threshold that we set.
“And that’s really unfortunate because the two countries that we would like to be opening up to, in terms of international travel, are the UK and the US, given the integration between our economy of those two countries and of course the number of visitors that would like to come here to spend money in hotels and have holidays here and so on.
“So, I think it’s very unlikely that either the UK or the US will be on that green list.
“It’s not going to be a particularly long list.”
Ireland’s plan to roll out its green list comes as the country’s Government continues to advise citizens not to travel abroad for holidays this summer.
But those who do choose to visit countries on the green list will not be required to quarantine themselves on their return.
Ireland still has a relatively low number of recorded coronavirus cases, with fewer than 26,000 infections having been confirmed in the country since the pandemic erupted.
Ireland’s National Public Health Emergency Team on Friday confirmed that an additional 34 cases of Covid-19 had been recorded in the previous 24 hours.
Three more people had also died after contracting coronavirus, the team confirmed, taking the country’s overall death toll to 1,752.