The Republic's health minister said his department was "preparing options" to present to government.Read more
An air-bridge between Guernsey and Iceland is no longer being actively pursued, Deputy Gavin St Pier has said.
Deputy St Pier said the country had seen an increase in the number of coronavirus cases, meaning discussions were "not progressing".
Similarly, discussions with the Faroe Islands have been halted due to a rise in cases.
Guernsey currently has one air bridge formed with the Isle of Man, allowing residents to travel freely between the two islands without the need to quarantine.
Deputy St Pier said the States would keep an "open-mind" to other jurisdictions "that could potentially form the same relationship".
People travelling to Guernsey via the UK will have to declare if they have been to any other countries in the last 14 days.
Under the new border controls, countries will be categorised into groups A, B and C, based on their quarantine requirement.
It means a person who begins their journey in a Group A country, but travels via the UK, will have to self-isolate for 14 days on arrival in Guernsey.
Deputy Gavin St Pier said border staff will use information provided by the person in their traveller registration form to issue advice.
Anyone who makes a false declaration will be committing a criminal offence, he added.
Improvements are due to be made to States technology to aid border staff in looking at arrivals recent travel.
The category of a country under Guernsey's new border controls could change depending on the situation of the region, the director of Public Health has said.
Countries will be categorised into Groups A, B, and C based on their quarantine requirements from 17 August.
Dr Brink said these groups could change "at short notice".
She said the States would provide the public with "appropriate information" to ensure they can make "the right decisions for themselves".
The Isle of Man is considering implementing similar border controls to those announced by the States of Guernsey on Wednesday, according to a senior Guernsey politician.
Passengers arriving from specific countries into Guernsey will be allowed to self-isolate for seven rather than 14 days following a negative test result, Deputy Gavin St Pier announced.
The island formed an air bridge with the Isle of Man in July, allowing people from both islands to travel freely between the two regions without the need to quarantine.
No date has been set for when travellers will be able to enter Guernsey without the need to quarantine.
Deputy Gavin St Pier, the Chairman of the Civil Contingencies Authority (CCA), has announced the self-isolation period for some travellers would be cut to seven days from 17 August.
He said those who had hoped for unquarantined travel from September would be "disappointed".
The seven-day test forms part of phase 5b in the island's lock exit strategy, and unquarantined travel would constitute phase 5c.
Phase six will eventually mark a "complete return to pre-covid travel norms", Deputy St Pier said.
He added that the CCA "must continue to plan and resource up so that when the time is right we can move very quickly to unquarantined travel".