Asked whether Canada might shut its frontiers to Europe or the United States, Trudeau told CTV: "We have taken some very strong measures and we are not taking anything off the table."
So far at least 249 Canadians have tested positive and one person has died.
Canada's public health agency on Sunday posted an advert for nurses, citing "an urgent need."
Nurses were needed to manage and control communicable diseases and make determinations about the risk to public health posed by foreign visitors, it said.
The premier of Quebec, Canada's second most populous province, called on Trudeau to seal off the country.
"It's not a good idea to continue attracting foreign tourists to Canada," Francois Legault told reporters on Sunday.
Legault also ordered the temporary closure of businesses where people gathered, such as swimming pools, bars, gyms and libraries. Restaurants can stay open but only at half capacity.
Canada has already boosted monitoring at airports and is urging its citizens to return from abroad while they still can.
"We're hearing the concern people have had. The shift in posture in the United States of course gives us significant things to think about," said Trudeau, who will address his cabinet later in the day.
Closing borders could have a major economic impact, given that Canada sends 75% of its goods exports to the United States.
All 10 of Canada's provinces have now reported cases of coronavirus, many linked to foreign travel.
Asked whether people visiting from abroad might be obliged to go into isolation, Trudeau replied: "We are considering everything."
The Liberal government will make significant fiscal announcements early next week to help Canadians and businesses hit by the outbreak, he added. The government is mulling a multibillion-dollar package for industries most hit by the outbreak, a source told Reuters on Friday.
Trudeau, asked about instances of people hoarding foodstuffs and toilet paper, said supply chains were intact.
"Not panicking about anything is going to be really important," he said.Trudeau spoke from his residence, where he is in self-isolation after his wife Sophie tested positive for coronavirus. Trudeau said he and his three children were "doing fine," while Sophie was feeling "under the weather."