With the number of coronavirus cases growing exponentially in Canada and the United States, the National Hockey League's chief medical officer says the pandemic is "really just entering the rapid acceleration phase" in North America.

Dr Willem Meeuwisse told nhl.com last week that the league is closely monitoring daily reports while evaluating several scenarios for resuming the season, which was paused on March 12 amid concerns about the pandemic.

"It's difficult to predict where the pandemic is going and what the timeline will be, but we expect this is going to get worse before it gets better," Meeuwisse said.

So far, only two NHL players－both of the Ottawa Senators－have tested positive for the virus.

"We have a pretty good idea now that the likelihood of more players being infected prior to the isolation period is pretty low," Meeuwisse said.

"That doesn't mean that somebody can't be exposed now, and I would expect that as this disease progresses and becomes more endemic that we're going to see more tests in players."

The NHL has directed players, coaches and league staff to self-quarantine through April 4, and deputy commissioner Bill Daly said "as we get closer to the date, we're going to have to make decisions as to our next step. We're biting this off in chunks."

Meeuwisse said he is in regular contact with his counterparts at Major League Baseball, the National Football League and the National Basketball Association "just to see how the guidance we're getting from our different experts aligns and to make sure that we're consistent in the information that we have, given that it's constantly changing".

As for what it would take for the league to finish its regular season and start the Stanley Cup playoffs, he said several factors would come into play.

"The specific circumstances are obviously going to depend on the pattern of the disease and the specific risks at that time," Meeuwisse said.

"That's one of the difficulties. This thing is changing daily, and guidance from health authorities is changing daily based on the changing circumstances.

"If we think about bringing people back together, we'd want to have some confidence that the players are healthy, some confidence they were not infectious at that time, and that bringing them back together, even in small groups, would not increase the risk of contracting or transmitting the coronavirus.

"And then we'd have to place that in the context of the larger society and the fact that we have people in 31 different market cities and they're likely to differ from one city to the next."

Daly said the league would have to evaluate each team's unique situation.

"We have to try to do what is competitively fair to all the clubs and the players, quite frankly, as we continue to hold out hope that at some point we'll be able to resume play," said the deputy commissioner.

"As with everything else, we're going to have to kind of see how it all develops, and if there are anomalies we're going to have to try to work our way around them in ways that are sensible. I'm only going to be able to determine what's sensible in those situations at the time and knowing what the circumstances are."

In the meantime, the world's best hockey players are being encouraged to stay in shape as best they can.

"We are allowing players to exercise outdoors, so they could be running or doing other things as long as they are not in proximity to other people," Meeuwisse said.

"If they can maintain some base conditioning in that way, then when they do come back together, we anticipate they'll go through some phases like conditioning first and practicing second or some kind of training camp that will allow them to get to game shape again before resumption of play."