Though Joseph is not confirmed as having signed with the southern franchise, he has indicated he is willing to take on the position, and will get into his work immediately.
Joseph (40) was about to begin his third provincial campaign as Wellington coach but signing with the Highlanders means he will have to give up that position because of New Zealand Rugby Union directives.
The national union does not allow head coaches of franchises to coach at provincial level.
When Glenn Moore was appointed head coach of the Highlanders in 2007 he had to give up his involvement with the Otago side, while Pat Lam had a few weeks to wind down his involvement with Auckland after he was appointed the head coach of the Blues in 2008.
It would be tough on Joseph to have to step aside at Wellington with the side to play its first game in the ITM Cup against Tasman on August 1.
Highlanders chairman Ross Laidlaw said an announcement on the coaching role would be made by the end of the week, and "nothing had happened yet".
Only the head coach would be named and it could take a while before a decision on the assistant coach was made.
There had been speculation Southland co-coach Simon Culhane would be Joseph's right-hand man, but he does not appear to be keen to head north.
The new coach would have some say as to who his assistant would be, Laidlaw said.
Wellington has begun its search for Joseph's successor, and assistant coach Andre Bell, like Joseph a former Otago player, looms as the favourite.
Wellington Rugby Football Union chief executive Greg Peters told The Dominion Post the union was aware of possible changes to the Wellington coaching position.
"We are fully aware of Jamie Joseph's situation with respect to the Highlanders' head coach position," Peters said.
"He has applied for the job with our full knowledge and full support, and should a move eventuate we will work through the transition process in due course."
All Black assistant coach Steve Hansen had been touted as being involved with the Highlanders, but any input would probably be at an advisory level, working with the Highlanders and the Crusaders.