Australia's Courier-Mail newspaper reported Queensland Rugby League approached the NRL recently to inquire about the prospect of Taumalolo quitting Tonga to play for the Maroons this season.
Taumalolo walked away from playing for New Zealand two years ago, which gave Queensland hope he might be eligible for them given he now plays for second-tier nation Tonga.
Only players available for selection for Australia can be selected for Origin.
Taumalolo has previously worn a green-and-gold jersey, playing for the Australian Schoolboys as a 16-year-old before being picked for the Junior Kiwis.
But the bold bid for one of the game's premier forwards was vetoed by the NRL, which ruled the North Queensland Cowboys player ineligible for Origin because he played 10 tests for New Zealand, a tier-one rival to Australia, the Courier-Mail reported.
An NRL spokesman told the Courier-Mail Taumalolo will never be able to play for the Maroons, despite living in Queensland for 12 of his 25 years.
"Under current RLIF (Rugby League International Federation) rules around eligibility, players cannot represent two tier-one nations," he said.
"If Jason Taumalolo were to play for Queensland, he would need to make himself available for Australia."
Queensland coach Kevin Walters was understandably disappointed by the ruling.
"We had some interest but Jason isn't available," Walters said.
"You want the best players playing Origin, but they need to be eligible and available.
"I wasn't aware of it [making Taumalolo eligible for Queensland] initially. But then I spoke to a few Queensland players and they made me aware of Jason's interest.
"Jason was weighing up Queensland a few years ago. He met with Mal and he decided to stick with New Zealand and he eventually played for them.
"He would have looked good in Maroon, certainly, but we have plenty of good forwards to choose from."