Australian Treasurer Joe Hockey is hinting Australia may change some rules that disadvantage New Zealand residents in Australia after the issue was raised by Prime Minister John Key.
"Prime Minister Key raised with me a number of issues. I think we can move on some, but let me go back and speak with my colleagues," Mr Hockey said on TV3's The Nation programme on Saturday.
"There were a couple of issues in welfare that I think the prime minister put a pretty convincing case," he said.
Mr Hockey said he would not go into the "shopping list" but he would look at the cost of possible moves.
"I will go back and have a good look," he said.
Mr Hockey was in New Zealand last week for an annual trans-Tasman meeting.
Mr Key has said he raised welfare for Kiwis resident in Australia with Mr Hockey and "got the impression they might deal with a few areas".
When Mr Key met Australian Prime Minister Tony Abbott in Sydney in February he didn't get anywhere on the issue.
An estimated 300,000 New Zealanders are living in Australia on special category visas. They pay taxes but aren't able to access benefits such as welfare, disability care and social housing.
Mr Hockey pointed out many New Zealanders living in Australia were not Australian citizens.