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Jordan takes the All Blacks' positive Covid cases to six after head coach Ian Foster, forwards coach John Plumtree and defence mentor Scott McLeod, and Crusaders midfielders David Havili and Jack Goodhue were ruled out.
Jordan was expected to start on the right wing in Saturday's opening test against Ireland at a sold-out Eden Park. His absence is likely to open the door for either Crusaders teammates Sevu Reece or Leicester Fainga'anuku, the latter on debut, to take his place.
Crusaders first five-eighth Richie Mo'unga was also absent from Tuesday training with a tummy bug. He may recover in time but, if not, Blues playmaker Stephen Perofeta could be called onto the bench to make his test debut.
Havili, who tested positive yesterday, was also expected to start at second five-eighth alongside Rieko Ioane in the All Blacks midfield but Quinn Tupaea may now benefit from his and Goodhue's respective absences.
Crusaders centre/wing Braydon Ennor has been called into the squad.
The All Blacks' preparations for the Ireland test were already compromised after the initial outbreak, with Foster calling on Joe Schmidt to help the team prepare this week following the positive tests among the coaches.
Foster says it makes sense to call in Schmidt, who would be joining the All Blacks after the Ireland series.
"Joe will come in for Tuesday and Thursday's trainings this week, and we're really grateful to have his help.
"We've planned for this kind of disruption and we've got back up plans and people on standby. Joe was one of those people we could call on.
"I've got every confidence in our coaching group, and in our senior leaders who are all stepping up in what's a massive test for us.
"Everyone has had to deal with these kinds of disruptions over the past couple of years. This is a real opportunity for the coaching group and team to pull together."