Tupou and Staggs were the two most notable selections in a 25-man squad announced by Woolf on Wednesday, with other Blues contenders Siosifa Talakai, Keaon Koloamatangi and Haumole Olakau'atu also called up.Â
The pair have until Sunday to make a choice between Tonga or the Blues, should they be selected by NSW coach Brad Fittler.
"What we don't wish to happen is that players who have this dual eligibility are not picked in one squad and then miss out on being available to play in another team," said Woolf, who has named Staggs at five-eighth for next Saturday's game at Mt Smart Stadium.
"If as many of our players as possible are playing representative football next week the stronger our World Cup squad will be."
The squad is rounded out by some of Tonga's most experienced campaigners including Jason Taumalolo, Addin Fonua-Blake and Tevita Pangai Jr.
Woolf has been unable to get time away from his club duties with St Helens and will hand the reins to Dean Young and Wayne Bennett as they take on a New Zealand side coached by Michael Maguire.
The game, which will be Maguire's first since his sacking by the Wests Tigers this month, could result in Ronaldo Mulitalo making his international debut.
The Auckland-born winger found himself at the centre of an eligibility storm last year when he was told 24 hours out from his debut for the Maroons that he didn't pass the criteria to play for Queensland.
Maguire has opted to overlook Shaun Johnson after his underwhelming return to the Warriors this season, with Dylan Brown, Jahrome Hughes and Kieran Foran jockeying for a role in the halves.
Brisbane's Te Maire Martin, who only made his return from a bleed on the brain this season, could also be a playmaking option.
Alongside Brown and Mulitalo, Marata Niukore, Jordan Riki, Scott Sorensen, Griffin Neame, Moses Leota and Erin Clark are all chances to play for New Zealand for the first time.
The Test is the first professional game of rugby league in New Zealand since the start of the COVID-19 pandemic.
"This squad has an exciting mix of fresh talent and experienced Kiwis having some of their best seasons," Maguire said.
"Some difficult decisions have had to be made, but it's a positive sign of our depth in certain positions."
KIWIS SQUAD:
Nelson Asofa-Solomona, Jesse Bromwich, Kenny Bromwich, Dylan Brown, Erin Clark, James Fisher-Harris, Kieran Foran, Peta Hiku, Jahrome Hughes, Moses Leota, Isaac Liu, Joseph Manu, Te Maire Martin, Ken Maumalo, Ronaldo Mulitalo, Griffin Neame, Briton Nikora, Marata Niukore, Isaiah Papalii, Jordan Rapana, Jordan Riki, Brandon Smith, Scott Sorensen, Joseph Tapine, Dallin Watene-Zelezniak.
TONGA SQUAD
Talatau Amone, Andrew Fifita, Addin Fonua-Blake, Moeaki Fotuaika, Siliva Havili, Tevita Pangai, Eliesa Katoa, Isaiya Katoa, Sione Katoa, Keaon Koloamatangi ,Tolotau Koula, Soni Luke, Joe Ofahengaue, Haumole Olakau'Atu, Will Penisini, Kotoni Staggs, Moses Suli, Siosifa Talakai, Tevita Tatola, Siosiua Taukieaho, Jason Taumalolo, Starford To'A, Christian Tuipulotu, Daniel Tupou, Sitili Tupouniua.
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