Wales captain Sam Warburton is expected to be fit enough to play against world champions New Zealand on 11 June.
Cardiff forward Warburton, 27, has been sidelined since suffering a shoulder injury on 30 April and missed Sunday’s 27-13 defeat by England.
Prop Paul James will miss the first Test match at Eden Park with a calf injury, but coach Warren Gatland hopes he will face Chiefs on 14 June.
Wales have not beaten the All Blacks in 26 matches since 1953.
Lock Luke Charteris will join up with the Wales squad on Saturday after being released by French side Racing 92.
Charteris and Clermont Auvergne centre Jonathan Davies both missed the defeat at Twickenham because they were on club duty, though Davies has already joined the Wales camp in New Zealand.
Hooker Ken Owens will also be ready for the game after overcoming a back problem.
Second-row Alun Wyn Jones is in line to win his 100th cap for Wales at Eden Park.