Katoa is expected to spend the rest of the week in New Zealand after suffering a brain bleed and seizures following his side's Pacific Cup loss to the Kiwis.
The NRL is continuing to gather information, in particular on the accidental hit to the head Katoa copped in a warm up from teammate Lehi Hopoate.
Tonga officials conducted an on-field check of Katoa after the blow, but deemed he did not require a full head injury assessment.
The 25-year-old was later taken for a HIA after a clash in the first half, before copping another head knock in the second stanza.
It was after the blow in the second half that the Melbourne second-rower began to fall ill and he eventually required an oxygen mask before being taken to hospital.
The NRL hope to conclude its findings on the matter next week, but is yet to consider whether changes to the protocols need to be made.
Currently, NRL clubs are required to have a spotter at all contact training sessions, monitoring head knocks as well as a camera fixed on players for review.
There are also spotters on the sideline at matches as well as an independent doctor in the bunker, with officials able to review replays of head knocks.
But there are no such requirement for video recordings of a warm up, which usually involve light running drills and work with tackling bags.
The independent doctor is also not responsible for picking up head knocks in the lead up to the match, with no feedback to the bunker monitoring warm ups.
Katoa's collision with Hopoate at Eden Park on Sunday was only captured on camera by chance by the host broadcaster, before it was replayed in the television coverage.
Tonga officials are adamant their medical staff did not see the replay of the incident until after fulltime and had not viewed the footage when they assessed Katoa the first time.
Katoa's incident is the first known serious head knock in a warm up since the NRL's concussion protocols, but there are no suggestions it  could have been foreshadowed.
NRL rules state players must not return to the field after going off for two HIAs, given concerns over multiple head knocks.
Had Katoa been taken for a HIA in the warm up, it is unclear it would have prohibited him from returning after the knock in the first half.
The Rugby League Players Association are also looking into the matter and are backing the NRL to conduct a thorough review before making recommendations.
"It is important that the NRL completes a thorough and detailed investigation, which the RLPA is advocating for and we believe the NRL are rightly taking this very seriously," RLPA chief operating officer Luke Ellis said.
Tonga coach Kristian Woolf supported his doctors over the incident on Sunday after the game.
"We have two very experienced doctors there, they have done the usual (tests). He has passed all that and passed it well," Woolf said.
"My job is not to question doctors.
"They were both comfortable with that and comfortable with him coming back on to the field."
