A fresh bid from Mr Jackson's National Urban Maori Authority (Numa) is likely to be the successful bidder. The bid is led by Mr Tamihere.
The authority is a collective of urban Maori groups, including Mr Tamihere's Waipareira Trust in West Auckland.
The Whanau Ora programme distributes health and social services funding at community level. It is open to all, but has a focus on Maori.
The money is now distributed by the government but in the contracting-out process is intended to become the responsibility of three providers - for the North Island, South Island and Pasifika.
The document issued by Te Puni Kokiri (the Ministry of Maori Development) set the level of funding available throughout the country at $20 million to $25 million.
A document leaked to the Herald showed the initial Numa bid fell flat after it over-reached on the amount of money required.
Te Puni Kokiri said it had "been assessed as providing insufficient value for money" and it needed to bring down the price of administering the distribution of funds.
The document said the proposal was based on getting $21 million.
Of this, $1.7 million was to be spent on staff, $3.3 million on operating costs and more on governance.
TPK said the contract bid should be reduced from the $5 million in costs sought to $2.3 million at most.
It asked the authority to reduce its estimated $2 million cost to set up the distribution scheme.
TPK also raised doubts over $1 million sought to pay for IT systems, and asked Numa to consider the scale of the IT investment.
It was also asked to explain a budgeted 20 per cent "contingency margin" - a cash cushion for unexplained costs - and pointed out an error in calculations which increased the cushion to 40 per cent.
Under the bid, Mr Tamihere's Waipareira Trust was to be subcontracted $260,000 to handle "back office" functions for the Whanau Ora deal. It received $130,000 last financial year for doing similar work for the authority.
Mr Jackson said he could not comment about the contract but described Mr Tamihere as the lead negotiator.
He confirmed Waipareira Trust's role providing support, saying the current arrangement for Numa had reduced fees.
Ngapuhi leader Sonny Tau said a competing bid had been made on behalf of the Iwi Leaders' Forum.
Whanau Ora contract
*Bid by Willie Jackson and John Tamihere to distribute taxpayer money for Whanau Ora is rejected.
*Their bid, with an estimate of $21 million, was considered too high.
*Te Puni Kokiri document says level of funding for the whole country was $20-25 million.
*A new bid by Mr Jackson's National Urban Maori Authority has been made, and the contract to distribute the Whanau Ora funds will be awarded this week.
Read previous stories on John Tamihere's recent tribulations here.
