The board's trust deed - set up in 1955 - gives the Crown the option to appoint five out of a possible nine trustees.
Newsroom reports that the Government is offering to change the deed to give control to Auckland Council but that the local authority does not want to take that on.
"This offer was based on the understanding that the Crown had no further residual or financial responsibility for the park," Newsroom quotes a departmental paper from February saying.
The issue has been playing out for at least four years after Auckland Council agreed in principle to take a controlling interest in Eden Park in February 2013.
Documents released to Newsroom said Auckland council chief executive Stephen Town wrote to the Government about the stadium last December:
"You will be aware of the Mayor's stated views on Eden Park and the opportunity to create a new stadium in a more central and user friendly location," Newsroom reported Town saying.
"Despite the very generous financial contributions from the government and the council, Eden Park does not have a viable long-term future as it is not able to fund depreciation or pay down its debt while its operating environment remains constrained... we do not believe Eden Park can trade its way out of the current situation without ongoing financial support from either the government or the Council, and even then the stadium will continue to have limited use.
"The council is open to having a discussion on how we move forward. Auckland requires a stadium of an appropriate size that has the capacity to host events that are not severely constrained by locality or consenting conditions. Auckland is also the natural choice to host New Zealand's national stadium, which would cater for a future Rugby World Cup or similar major sporting event, Town said the documents obtained by Newsroom.
In March Goff commissioned work for a new central city stadium costing up to $1 billion.
"We need to know what the options are for potential stadium sites in Auckland," Goff told the Herald at the time.
"This is not something I see as being a priority burden on ratepayers."
The mayor said the council needed to find alternative ways to fund a new stadium, which could cost up to $1b.
They included contributions from major sporting codes, income from concerts, private sponsorship and selling assets, like Eden Park.
"The option of rebuilding Eden Park is still live but we need to know what other sensible alternatives exist to make the best decision for Auckland," Goff said at the time.
