Australian Anzac Frigate Replacement, page-2

There's an interesting couple of lines in yesterdays ann of the delivery of combat ship 6.

“Our workforce continues to demonstrate superior design, construction and execution building the Littoral Combat Ship. The program is well positioned for a smooth transition from LCS to frigate.”

So I am assuming they would be contenders if given the opportunity.
I guess it will have a lot to do with how the politics plays out. However, the size and success of the ASB contract with the US Navy must be an excellent card to have in your kit.

http://www.aspistrategist.org.au/future-frigate-interoperability-through-partnership/

Above is a link to an article in "The strategist" by Michael Ward
Greater interoperability between RAN and USN will deliver a sustainable and cost-effective operational advantage against the background of our convergent strategic interests in the Indo-Asia-Pacific. While there’ll be challenges for Defence in implementing this approach the benefits can be realised through strategic partnering between Defence and industry that makes use of the sector’s historical investment in systems engineering and integration. Our combined experience can serve to future proof us as we traverse this growth path. Michael Ward is the managing director of Raytheon Australia.

There is a heap of speculation on that site about what and who and where.