Leo Varadkar has expressed concern over Stormont sticking to UK foreign travel arrangements.
The Tanaiste also admitted plans to monitor people travelling into the Irish Republic from countries not on Dublin's "green list" needs to "tighten up".
He told RTE's the Week in Politics: "We're going to look at other measures as well, for example, the possibility of requiring people to have evidence of a negative (Covid) test prior to travelling from some countries."
He raised concern that holidaymakers from Northern Ireland are allowed to travel to 59 countries without having to quarantine on their return, while the Republic's "green list" features just 15 nations.
Earlier this week Stormont Health Minister Robin Swann asked his cross-border counterpart to consider new laws and data-sharing agreements to help track international travellers arriving on the island. But Mr Varadkar said Stormont has been "very clear" it does not want to have an all-island approach to its travel arrangements.
He said it will be one of the issues discussed at this week's North-South Ministerial Council meeting in Dublin.
He added: "Certainly in any conversations that I had with the First Minister (Arlene Foster) and anything she said since, they've been very clear that when it comes to travel they want to stick with the common travel area with Britain and won't be restricting travel between Britain and Northern Ireland."
Meanwhile, the plan to reopen schools in the Republic will see extra teachers, extensive cleaning regimes and personal protective equipment put in place, Mr Varadkar said.
The Department of Education has been finalising details in its planning document before it is brought to Cabinet today. The Irish Government is aiming for full reopening of schools at the end of August. Mr Varadkar said he has read the document in recent days and is "confident" students and teachers will return by the end of next month.
A Co Antrim couple due to fly out to Spain yesterday had to cancel their holiday at the 11th hour after the country was removed from the quarantine exemption list at short notice.