"They have a unique position where they have got some very large profitable projects and they might want to think about the mixture of those assets," he said.
Mr Carter said the council should sell some of its shares in Christchurch Airport and the Port of Lyttelton to fund the quake rebuild, avoid further debt and keep rates at an acceptable level.
Mr Carter said the move would go a long way to paying for the council's share of the rebuild, which stands at just over $1.3 billion.
"We had a significant amount of our fundamental services destroyed in the earthquakes. The extent to which the Christchurch City Council has covered itself with insurance hasn't been revealed, but clearly they are going to need to raise a lot of capital to rebuild many of the Christchurch facilities," said Mr Carter.
Mr Parker said that even after borrowing and proposed rates rises, the council would still have one of the lowest levels of debt of any council in New Zealand.
He told National Radio the Government hadn't used special powers under legislation created after the earthquakes to force the council to sell its assets.
"If the Government decides to go down that path we'll talk about that if and when it arises," said Mr Parker.
He did not back the Government's asset sale agenda and said the council's assets brought $40 million a year in dividends.
"Our community would prefer to hold onto our strategic assets and to borrow and to spread those borrowings for the elements of the rebuild that are not met by insurance, or by a government grant. Over a couple of generations we think that's a fair way to spread the costs and keep it as affordable as possible," he said.
In January Earthquake Recovery Minister Gerry Brownlee signalled the Government would encourage asset sales when he asked for a list of council-owned assets.
Mr Carter said the Government was keen to see all councils look at asset sales to keep rates rises in check and reduce debt.
in a statement today, Len Brown reaffirmed that Auckland would not be selling off its strategic assets - the port and its airport shares.
"One of the biggest pressures we face is the costs around the amalgamation of Auckland Council, and that is a cost imposed on Auckland by the Government.
"Our core strategic assets will not be sold. Generations of Aucklanders have invested in them and they want them retained in public ownership. They bring in tens of millions of dollars a year, taking pressure off rates. Past assets sales have delivered very poor results. We do not intend going down that path," he said.
But Auckland Council was considering the sale of non-strategic assets such as property, which could provide as much as $400 million dollars in revenue for ratepayers, he said.