All Blacks second row Sam Whitelock is a doubt for the first test against Wales in Auckland on Saturday, 11 June.
The 27-year-old is recovering from a hamstring injury suffered playing for Crusaders in Super Rugby.
New Zealand are already without experienced campaigners Richie McCaw, Dan Carter, Ma'a Nonu and Conrad Smith who have quit international rugby.
"It's getting better, we've just got to take it day by day at the moment," said 73-times capped Whitelock.
"I'm just icing it and then keeping it warm, and taking things slowly," he continued.
"I just have to be mature. A lot of the outside backs are saying to me that if you blow it to pieces again it's not real good."
Warren Gatland's Wales side play three tests against New Zealand this month as well as a midweek match against Waikato Chiefs on 14 June.
Wales have not beaten the All Blacks in 26 matches since 1953 while the Auckland test will be New Zealand's first match since beating Australia 34-17 in the 2015 World Cup final.
How will Kiwi's cope without McCaw and co?
The retirement from international rugby of legends like double-World Cup winning captain McCaw and fly-half Carter means the All Blacks are in the process of rebuilding.
Coach Steve Hansen prefers the term re-establishing and flanker Jerome Kaino says there the player's cannot afford to dwell on missing players.
"We don't want to look back and keep missing the guys who used to be there otherwise we'll always be trying to fill holes that they've left," he said.
"We want to create paths for ourselves. We need to start where we finished last year and keep hitting up instead of looking back all the time and wondering what they would do."
|Wales' summer fixtures:|
|11 June: New Zealand (Auckland)|
|14 June: Chiefs (Hamilton)|
|18 June: New Zealand (Wellington)|
|25 June: New Zealand (Dunedin)|
Kaino is also impressed with the Wales back row - although the tourists will be without injured pair Dan Lydiate and Justin Tipuric.
"Toby [Faletau] is one of the most damaging ball carriers in world rugby at the moment but also Sam [Warburton] does a lot of the hitting stuff."
He works hard as a number seven and as a skipper and is definitely a strength of their side.
"We've got our work cut out in the loose forwards - but we've got three tests to try and figure them out."