The only company to put its hand up for AMI so far could get a clear run at the troubled insurer if competition rules shut out bigger industry players.
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.
AMI is still trying to find capital from private sources to cover the shortfall between existing resources and expected earthquake claims. If it can't find the money, the Government's rescue package would kick in.
Tower says it is interested in re-capitalising AMI which would avoid the Government having to step in.
Analysts say the two biggest players in the general insurance market - IAG and Suncorp - could run into opposition from the Commerce Commission if they bid for AMI.
Tower, which has less market share and plenty of cash, says it would be interested if it could take full control of the company.
Analysts say private equity buyers are unlikely to bid because they would not get the sort of cost savings that insurers would from a merger.