The Government is considering ramping up checks on people arriving in Ireland from overseas to ensure they are quarantining for two weeks.
The move could see gardai call to hotels where tourists are staying after arrival to make sure they are self-isolating.
It comes as the Cabinet will decide today if the remaining pubs should stay shut after the National Public Health Emergency Team (NPHET) raised concerns about allowing them to open on Monday.
Of the 250 pubs yet to open in Dublin, 225 would reopen next week if given the go-ahead.
Increasing spot checks on people arriving in Ireland is among a number of measures being considered to stop the spread of Covid-19 from overseas.
People arriving from abroad will be given strict instructions on quarantine rules and told it is illegal to give false information on passenger location forms.
There are also plans to increase the number of people to check visitors arriving at airports and ports, along with more signage.
Rapid access to testing for people coming to the country could be introduced too.
A government source said it plans to "scale up" follow-up checks on people who fill out the passenger location form to ensure they are staying where they said they would be for two weeks.
Those found to be not staying where they said they would be face paying a fine.
Meanwhile, fresh doubt hangs over whether up to 3,750 pubs which serve only alcohol will be allowed to open from next week amid heightened fears of a rise in infections.
Couples planning to get married in the coming weeks may also have to cut down on their wedding guest list.
The number of new people diagnosed with Covid-19 jumped to 32 yesterday, the highest daily toll since mid-June.
There were no deaths from the virus, but there is growing unease at its spread over the past two weeks, reversing a downward trend.
The NPHET, which met yesterday, is understood to have signalled its unease at moving to the fourth stage of the government road map.
This would not just impact pubs which serve only alcohol but also nightclubs and the number of people attending mass gatherings.
Any stalling would affect the size of weddings and halt plans to increase attendances to 100 people for indoor events and 500 outdoors.
It means the Government is facing a major dilemma, risking inflicting a financial blow to many small pubs which have been shut down since March.
The Government will have to justify why it will allow people to travel abroad to green list countries such as Greece, where Irish holidaymakers can enjoy a drink in a tavern with the risk of infection it entails, but deny customers who stay at home an outing to their local pub.
A spokesman for the Vintners' Federation of Ireland, representing around 3,500 publicans who are waiting for the news, said last night: "We need clarity.
"The publicans have been closed for four months and have been shabbily treated with no guidelines on reopening.
"It is a terrible way to treat them."
A government source said last night: "NPHET will give their advice and the Government will make their decision."
Central to their concern is the spread of the virus among younger people who are more likely to go to pubs or attend mass gatherings.
However, recent evidence also shows that the lack of pubs has led to many more house parties.
These include a recent party organised by a group of young friends from around the country in Killarney, which has led to a cluster of infections.
Speaking in the Dail, Taois- each Micheal Martin said he was more concerned about house parties than pubs re- opening.
"What is of more danger than anything is a situation where we have 30 or 60 people at a house party or parties taking place on certain roads in our cities, and we will have to do something about that," he said.
Acting Chief Medical Officer Dr Ronan Glynn said: "Knowing the symptoms of Covid-19 and making contact with your GP immediately is a crucial component to us identifying and containing this disease.
"Symptoms associated with Covid-19 can be similar to other common ailments. I would urge anyone experiencing symptoms to assume it is Covid-19, in the first instance, until a GP or test tells you otherwise."
As of midnight on Monday, 523,277 tests have been carried out. Over the past week, 49,264 tests were performed and 57 tests were positive, giving a positivity rate of 0.3pc.