New Zealand Rugby says it will consider any request by players to pull out of the All Blacks Rugby Championship campaign on a case by case basis.
Australia was confirmed as the host of the revised 2020 Rugby Championship across November and December last week, meaning the All Blacks, along with the Springboks and Argentina, will be spending nine weeks away from home.
New Zealand Rugby chief executive Mark Robinson said they want to have the tournament wrapped up by early December.
"We want our players to feel happy safe and comfortable in the environments they are in ... we are like any employer we want to do the right thing by them and ensure they have the appropriate time to consider all the ramifications of being away for that period of time so we will just continue to work through that.
Asked on Morning Report if players would still be paid if they refused to go to Australia, Robinson was non-commital.
"We'll work through all those scenarios in due course."
Foster denies claims All Blacks players could skip Rugby Championship
Meanwhile, All Blacks coach Ian Foster told Nine to Noon that he has spoken with the players in question.
"The players have categorically denied that [not wanting to go].
"But we are having conversations with players to make sure that we deal with the family situations and we'll do that one on one with the people, we know that... we've got between now and until the end of October while we're in New Zealand to control some things in that space and how we actually integrate families into our programmes is going to be critical.
"But there is a harsh reality that the nine weeks looks like it's going to be nine weeks and we'll just deal with the situation as we go along, but I've had no player to this date say to me that they're not coming because of family, but I have had a lot of players with lots of questions and that's very natural because I think we've all got questions at the moment," he said.
Foster did admit though that players have told him they don't want to be away from home for nine weeks.
"I've had a lot of players say that, but that doesn't mean they won't be coming.
"You go to a world cup and you are away from your families for seven weeks, the difference is here is it's very hard to bring families in during the tournament... We'll treat that issue with the respect it deserves by talking to players about it but we certainly won't get to caught up with media speculation that players won't be coming.
"There will be an All Black team, at the moment, going over to play a Rugby Championship in Australia."
Foster said he thinks it is "highly unlikely" players will be able to brought in late or leave early, or families join them in Australia, due to logistical and health concerns associated with quarantine.
He said New Zealand Rugby was seeking clarity from the Australian government on whether that would change.
Earlier on Tuesday, the New Zealand government announced it would relax the quarantine rules for the Wallabies so the team could train while in managed isolation ahead of the Bledisloe Cup tests.
The change came after Wallabies coach Dave Rennie complained about the preparation time for the first test on 10 or 11 October.
Foster said it was good the two parties could reach an agreement.
"I think we've got a very equitable situation and there's no reason they [Wallabies] can't come over," he said.
Foster also believed if the government had sorted quarantine requirements for the Rugby Championship quickly, as it had with the Bledisloe Cup, he thinks New Zealand would be have ended up hosting the former.
"I certainly feel it would have put us in a stronger position... we've got the ability there, things are trending well, if we can get full crowds, if we could have solved the quarantine thing it certainly would have made our case a lot easier to sell."