Central to the proposal is bracing walls and tunnelling in to create a metal "safe haven" within the building to allow further work.
The church's Cathedral Project Group says it will review the trust's report "against the considerable work already undertaken".
The group said it had been told by its own engineers that the maximum retention option would cost more than $100 million.
"We had considered the possibility of safe havens but this approach was rejected," said acting dean Lynda Patterson.
The Government's Canterbury Earthquake Recovery Authority is requiring the church to make the building safe, which Mr Anderton says is taken care of in the trust's proposal.
The option of rebuilding from the existing structure might prove cheaper than demolition and rebuilding.
If a further $50 million or $60 million was required above insurance, Mr Anderton was confident it could be raised through national and international networks, without seeking money from the taxpayer.
Many Christchurch people were still too focused on things like their own quake-damaged homes to think about the cathedral.
But if it was demolished, in years to come, people would question why it could not be saved, Mr Anderton said.
A spokesman for Earthquake Recovery Minister Gerry Brownlee said it was now a matter for the church to "consider and discuss with the Great Christchurch Building Trust".
He said the authority was going to step back for the time being and give those parties time for discussion.