Having released Mat Rogers earlier this month, the ARU reportedly offered Tuqiri a Â£1.6million deal in a bid to keep him in the code.
Tuqiri insisted that money was not the reason for him rejecting the offer, stressing that he did not want to rush into what he describes as the biggest contract of his career.
"At this stage there are some key components that we spoke about but haven't appeared in the contract," he said.
"At the moment, the deal from the ARU isn't satisfactory, but you don't always knock over a deal at the first go."
"This is the biggest contract of my career and I want to get it right," Tuqiri told the The Sunday Telegraph.
Among those in the running for Tuqiri's services are Brisbane, Melbourne, the Sydney Roosters, South Sydney and NRL new boys Gold Coast, and he has spoken with Cronulla coach Ricky Stuart.