But he told the Stormont Assembly that this option was not “inevitable”.
Executive ministers are meeting to discuss proposals to help curb the spread of Covid-19 across the North of Ireland.
The Department of Health reported three further deaths and 1,469 new cases in the North of Ireland.
Last Thursday, Mr Swann advised anyone who worked from home when the pandemic began last year to do so again now.
His document also suggested introducing a “scores on the doors” Covid compliance rating for businesses.
Mr Swann said on Monday that “if the current trajectory continues with regard to the increased cases we are seeing, we may once again face the possibility where venues are asked to close their doors during the Christmas season”.
“But let me be clear, it is not inevitable and I do not want to have to re-introduce further restrictions unless completely unavoidable,” he added.
Mr Swann also expressed disappointment that some hospitality venues had not acted responsibly after social distancing rules were relaxed.
Decisions on whether to strengthen current mitigations must first be agreed by the Executive.
Health officials believe the proposals could help reduce transmission of the virus.
Justice Minister Naomi Long said on Monday that the Executive was “not planning for Christmas closures”.
“We started off in terms of looking at vaccine certification as one means of trying to ensure that we drive down transmission and as those who are in more high-risk environments are less likely to become seriously ill as a result, that’s one means of keeping the doors open on businesses,” she added.
“We’ve been considering the paper today around how we actually try to get the basics right and get people to comply with things like handwashing, wearing masks, trying to voluntarily reduce their number of close contacts, trying to ensure where people can work from home they do work from home.
“Our focus at the minute is not on closure but on trying to keep businesses open.”
On Monday, Deputy First Minister Michelle O’Neill said on Twitter that it was “vitally important that all Executive ministers work together to get us through this difficult period”.
“It’s time to redouble our efforts to limit the spread of the virus, protect lives and our hospital system,” she added.
Last week, the Department of Health warned that unless cases decrease significantly in the next three weeks, then more “severe” restrictions could be required before Christmas.
Stormont ministers have said they do not want to have to impose tougher mitigations that could damage trade.
They have already agreed to put in place proof of Covid status for certain sectors, which will become enforceable from 13 December.
The plan means people will have to provide proof of vaccination against Covid-19 or proof of a negative coronavirus test result to access nightclubs, pubs, cinemas, theatres and restaurants.
The DUP had voted against the proposals but Mr Swann and other Stormont ministers said the use of Covid status certification would save lives.
DUP ministers had said they wanted to see other measures explored by health officials, which could also help reduce the number of Covid cases.
At present, the Executive advice on working from home is that people should continue to do so where they can.Tags: