Robertson said he was keen to see the Government's banking spread among the banks and would look to do that at the next review in 2023.
"In order to be the government's banker there is a very sophisticated level of services that need to be provided, not every bank can provide that.
"One of the things I am interested in, and this did happen the last time the contract was there, was what services outside of the core services could be provided by other banks.
"I think it is a good thing we might have our services from other banks but to do that core set of services, the big payments and so on you need a very sound infrastructure. We will look at that, but that is the requirement."
Westpac has had the government's banking contract since 1989. It was last reviewed in 2015 and was opened up for tender after the Green Party agitated for years to have the banking services done by a New Zealand bank.
But Westpac still won the main contract to do all transactional services for eight years. It means there are 35 government agencies that have to use the bank.
Four other banks, including Kiwibank, were also awarded smaller contracts to perform other banking services.
Robertson dismissed concerns about Westpac selling its New Zealand arm to an overseas company.
"Well, obviously, we are at early days here. Westpac is looking at a range of options for its New Zealand branch. Bear in mind that it is already Australian owned."
He said it may open opportunities for other forms of ownership including New Zealand based ownership.
"What is important to me is that New Zealanders have access to quality, stable, banking services and we have got banking services that are New Zealand owned and we have got banking services that are Australian owned. The most important thing is that there is choice and it is quality choice."
Robertson said if Westpac New Zealand was floated on the sharemarket it would a great opportunities for New Zealanders to invest while also deepening the New Zealand capital market.