''We want to get them right before the South African series,'' coach Mike Hesson said today.
He wouldn't get specific on the nature of Williamson's foot problem, except he's had it for a while.
''He hasn't had time to rest it. I think you'll find everybody has got something wrong to some degree.
''When you play consistently, you're often playing with little niggles and when you do have a period of time to knock it on the head you've got to use it.''
Boult and Southee are having a week off to recuperate from heavy workloads ahead of South Africa's arrival next week.
Hesson also said test wicketkeeper BJ Watling and fast bowler Neil Wagner are racing the clock to be ready for the first test starting in Dunedin on March 8.
Watling is expected to be ready despite having knee and hip issues to get over; Wagner fractured a finger on his bowling hand in a Ford Trophy game last month.
''BJ is making reasonable progress. He needs a bit of time. Hopefully he'll get back for the last Plunket Shield round before the test,'' Hesson said. That will be ND's match against Otago at Whangarei starting on February 25.
The South African trip is big for Pretoria-born Wagner and Dunedin is his home ground.
''He's pretty determined to be right for the first test but we'll have to wait and see. It will be a huge blow for us if he's unavailable.''
The statistics back that assessment.
Wagner has taken 118 wickets in his 29 tests at an impressive 28. Trim that down to his last 11 tests, dating back to the Australian match at Christchurch a year ago. In those matches, Wagner has taken 51 wickets at a fine 22.3.
No wonder New Zealand will be sweating on his fitness.
It is a settled test seam bowling group and as Hesson pointed out some of the next level of bowlers are battling injury issues, such as Doug Bracewell.
Auckland quick Lockie Ferguson has impressed in his brief time in the New Zealand limited-overs teams this season.
''He's certainly in our (test) thinking,'' Hesson said.
''He's got through a lot of overs in the last couple of years in the Plunket Shield. He's quite sustainable and has a nice record. He does give us a point of difference.
''He is certainly asking to be considered but the test squad has been quite stable in recent times.''
That will change if Wagner doesn't make it to University Oval.