Mandatory quarantine for people travelling into Ireland without proof of being Covid-free and tighter north-south border Covid checks are to be considered by Government ministers meeting today.
The Government is likely to bow to pressure for new rules on quarantine.
The Covid-19 ministers' sub-committee will try to recommend a strategy to boost the trend of lowering virus cases and ease near-breakpoint pressure on hospital services.
But one Government source has conceded "there are still more questions than answers" about the detail of new regulations to be adopted.
The major stumbling block remains how to deal with people travelling in from Northern Ireland, who could seriously undermine a Dublin government plan to oblige people landing here to have a certificate issued within the previous 72 hours showing themselves to be Covid-free.
Taoiseach Micheál Martin has spoken with UK Prime Minister Boris Johnson over the weekend about a "two islands" joint approach to the issue of people travelling in from overseas.
"But anything which might come of that remains to be seen," one government source told the Herald.
Mr Martin said mandatory quarantine of up to five days may be considered for people travelling into Ireland without proof of a so-called PCR test delivered within the previous 72 hours.
But others in Government point out medical experts rarely view a five-day quarantine as sufficient and more usually insist on 14 days.
Last night officials said there is clear pressure on the Government to act.
"But three practical obstacles remain in the way. These are questions of accommodation, transport and how to enforce any such quarantine," said one source.
Officials in all three Coalition parties - Fianna Fáil, Fine Gael and the Green Party - insisted their leaders are united on the need for action but are still undecided on the practical implications of whatever extra restrictions they involve.
They expect some proposals will emerge later today to be put before Cabinet tomorrow.
Labour Party leader Alan Kelly has said a longer lockdown should be implemented to suppress Covid-19 along with a "national aggressive suppression strategy".
Speaking on RTÉ radio's This Week, he said the Border should be better policed to stop non-essential travel and that mandatory quarantine should be introduced for all visitors arriving here.
He added that it was inevitable that the Leaving Cert would be cancelled.