Speaking on behalf of DHBs, Hawke's Bay DHB chief executive Keriana Brooking said DHBs could not make a formal offer to the PSA before the weekend but aimed to do that in the coming days.
"We're an employer within the public sector so there are just a few things we need to square off and we're hoping to be in a position to move to formal offer very quickly early next week."
Brooking said a large number of allied health staff work in 80 professions across New Zealand.
"So for us, we have to plan that we cannot rely on them outside their set hours; however, we have other allied health staff that are not part of the PSA and we have other ways in which we are managing our work."
DHBs plan to make a formal offer to the union this week and hope to avoid a 24-hour strike planned for May 16.
The PSA says if the district health boards honour the Employment Relations Authority's recommendations - which are confidential - the union would be happy to put the offer to a vote.
An earlier round of strike action was called off during the Omicron outbreak in March, after the Employment Court ruled in favour of DHBs seeking an injunction.
- RNZ