Tanaiste Leo Varadkar has said that certain types of restrictions could be put in place if numbers continue to rise.
The Fine Gael leader said Dublin and Limerick could follow measures put in place in Glasgow where social visits to houses were limited.
He did however say that the mental health effect on people due to another lockdown is something they have to take into account.
Speaking on Newstalk Breakfast, the Tanaiste said: "If we do have to act we will act..but we won't do it without good cause.
"I have a real concern about the impact on business and jobs of new restrictions.
"The idea of restricting house visits in Dublin and other cities is an option we'll have to consider if the numbers continue as they are."
A total of 307 new cases were confirmed by the Department of Health on Tuesday - the biggest daily rise since May 14.
The Tanaiste however also said that the Government would like to allow more essential travel by Christmas.
Mr Varadkar added: "We would like to enable more essential travel, maybe allow some people to see their relatives this Christmas.
"You'll see in Heathrow they're trialing tests that get results in a few minutes."
