Outside back Jordan was in brilliant form in Super Rugby this season but joined his Crusaders team mates David Havili and Jack Goodhue in isolation after the positive test.
Coach Ian Foster and his assistants John Plumtree and Scott McLeod are also isolating after positive tests and former Ireland coach Joe Schmidt has been drafted in to help out with the All Blacks' preparations for Saturday's series opener at Eden Park.
Skipper Cane said Jordan was likely to miss the Auckland Test and the second match in Dunedin the following week but could play in the final game in Wellington.
"It's terrible timing for everyone who got COVID. We feel for Will but there is a lot of depth and competition for places," Cane told reporters after training on Tuesday.
"I don't know if Will was going to be starting or not, but I'd say he was a pretty good chance. It just means someone else will step up in his place and it's another opportunity for someone.
"Hopefully COVID doesn't knock him round too much. Realistically he's probably only a chance for the third test now."
Jordan has scored 17 tries in 13 appearances for New Zealand and scored 10 tries for the Crusaders during their Super Rugby Pacific-winning season.
New Zealand have a plethora of outside back talent to choose from, even without the fleet-footed Jordan, and Braydon Ennor has already been called up to cover for the possible absence of Havili and Goodhue in the centres.
Richie Mo'unga also missed training on Tuesday with a stomach bug, but he has not tested positive to COVID and is expected to rejoin the team later this week.
Cane said a similarly disrupted start to the Super Rugby season meant the players were used to just getting on with their jobs.
"The team has been really impressive," he said. "Maybe it's because we're so used to it throughout Super Rugby. We've just been rolling with the punches."
Foster will name his team for the first test on Thursday.Â
with The AP
