First minister Arlene Foster says it is “probable” that the new more infectious variant of coronavirus is already in NI.
She said four cases in NI are being tested to determine if they are the new highly infectious variant.
It comes as the Stormont Executive agreed that Christmas bubbles in NI should be limited to one day.
However, Mrs Foster said she did not expect police to be “knocking on people’s doors on Christmas Day”.
She said people should instead take “personal responsibility”.
Ministers met remotely on Sunday night to discuss the impact of the variant on Christmas rules.
The Executive said there would be flexibility on which day between 23 and 27 December people come together, to accommodate those working on Christmas Day.
The meeting also focused on travel from GB to NI, but nothing was agreed.
Health Minister Robin Swann is to consult with Northern Ireland’s attorney general about the legality of a ban on travel from Britain.
The Republic of Ireland is one of a number of European countries that have imposed travel bans on the UK.
Irish Minister for Transport Eamon Ryan said while the ban was for 48-hours he did not want to give anyone “false hope that there is likely to be any major change”.
He said the two day period allowed time to “assess the situation” and added that no border controls would be set up on the Irish border.
Mr Ryan said while his government would be making concerns about the lack of a NI-GB travel ban known, it would be up to Stormont to decide what to do.
BBC News NI understands that Sinn Féin proposed prohibiting travel from Great Britain into Northern Ireland and said it should be a matter of priority.
Sinn Féin wants the health minister to use powers from the 1967 Public Health Act to impose a ban on people from GB.
Speaking on BBC’s Good Morning Ulster, Mrs Foster said a full GB travel ban was not a “simple matter” and would have “downside consequences”.
She confirmed the executive would take legal advice from the attorney general about a travel ban.
Police will not be ‘knocking on doors’
But Mrs Foster said those living in the most infected areas are already prohibited from travelling, although she recognised some would try to “game” the regulations.
“There is a travel ban in place – it covers about 17m people in England, those people can’t come to Northern Ireland.”
Mrs Foster said the new bubble rules would be placed in law, but said she did not expect police to be “knocking on people’s doors on Christmas Day or Boxing Day to check they are abiding by the law”.
She said the four possible cases of the new variant they show “different sequencing” from other cases.
The planned relaxation of Covid-19 rules in England, Scotland and Wales was cut from the previously agreed five days to just one on Saturday.
‘Division at Stormont’
Stormont Ministers are divided over whether or not to impose a travel ban on people moving from GB to Northern Ireland amid fears about the spread of a new variant of the coronavirus.
With the new highly infectious variant of the coronavirus now out of control in London and other parts of England Stormont Ministers met last night to discuss how best to respond to the fresh threat.
Sinn Féin wants the Health Minister to use powers from the 1967 Public Health Act to impose a ban on people coming in from Great Britain.
But the DUP says those living in infected areas are already prohibited from travelling.
The health minister is due to consult with the Attorney General and bring a paper back to the Executive today.
But there was agreement among Ministers to cut the number of days three households will able to meet over Christmas from five to one, following similar moves in England Scotland and Wales.
A new six-week lockdown for Northern Ireland, coming into force at 00:01 GMT on 26 December, was announced on Thursday.
After restrictions were tightened in the rest of the UK, a statement from the first, deputy first and health ministers urged people to “think seriously about their plans for Christmas, and to now consider limiting their coming together to Christmas Day only”.