Insurance company Tower says it is very interested in becoming the sole owner of AMI.
The Government has put up a $500 million rescue package for the country's second-biggest insurance company in case it does not have enough money to cover all the earthquake claims in Christchurch.
Finance Minister Bill English said the package will only be called upon as a last resort, and once AMI's own resources have been exhausted.
AMI says it is now looking to try to raise more capital instead of using the bailout.
Tower chief executive Rob Flannagan says it possibly has the means to provide that capital injection, and has already held discussions with AMI.
"AMI is a good business and it's a very compatible business with Tower. We have very similar clientele and there are some good synergies, I think, between the two organisations.
"It is a very interesting proposition for us and we would like to explore it."
Mr Flannagan says AMI has plenty of cash to meet claims, but its problem is its capital requirement.
Tower is a New Zealand-owned company and would have more relevance in the marketplace if it aquired AMI, he says.