Boult and de Grandhomme were both part of the Black Caps squad which arrived in Perth on Saturday, with both under an injury cloud.
Left-arm quick Boult missed New Zealand’s Second Test draw with England due to a side strain, while de Grandhomme was also absent with an abdominal tear.
New Zealand bowling coach Shane Jurgensen said the pair are “progressing nicely” having completed a light fielding session on Friday.
Perth’s Optus Stadium is expected to offer plenty of pace and bounce for the quick bowlers, meaning Boult’s availability will be key.
Matt Henry replaced Boult in the Second Test against England, while Lockie Ferguson could come into contention to join Neil Wagner and Tim Southee in the attack.
“They are both going quite well,” Jurgensen said.
“Intensity wise at training, they were pretty similar. I think they are both going quite well.
“At this stage, they are hitting all their markers in terms of their rehab program.”
New Zealand last toured Australia for a Test series four years ago, losing the three-match series 2-0 but are a better side nowadays led by Kane Williamson, with Test ranking of second.
“We have quite an experienced group there compared to maybe four years ago when the team visited the shores for a previous Test series,” Jurgensen said.
“There is a reason why the guys have been playing good cricket and doing a great job as they are.”