"That's not the safety net assurance that we expect as New Zealanders when we travel abroad."
Mr Allen confirmed that was under consideration, "but only if it can be achieved in the context of diplomatic propriety and will provide a quality service to New Zealanders".
Mr Goff also understood New Zealand's diplomatic presence at the UN may be cut from 10 to six staff. Other cost-cutting measures already mooted included closing some embassies, including that in Stockholm.
Mr Allen said the ministry was considering "non-resident" ambassadors to other countries who would be based in Wellington but he declined to discuss other proposals before consultations with staff due to begin in two weeks.
Staff concern at the proposals has shown up in a survey by research firm JRA completed by 71 per cent of ministry employees late last year.
The survey revealed an 8 per cent drop in staff who had confidence in the ministry's leadership, which at 51.8 per cent was 10 per cent lower than the benchmark across the wider public service.
JRA said the largest decreases in survey scores since 2010 were related to organisation purpose, direction and values.
Fewer than half - 47 per cent - of employees believed the ministry was making the changes it needed to be successful in the future and only 32 per cent said the organisation was helping them to prepare for those changes.
Only 14.4 per cent of staff felt "engaged" with the ministry compared with 28.4 per cent who were disengaged and 57.2 per cent who were ambivalent.
"We knew we were running this survey at a time when the organisation was facing a particular challenge," Mr Allen said.
"Our decision to run it at that time was because we wanted to get actionable data from our people about the sorts of things we need to do better to actually make the change more effective."