Taumalolo made his test debut during the 2014 Four Nations and last played for the Kiwis in the 16-0 defeat to the Kangaroos in Newcastle in May.
Their inclusion brings the wider squad to 32, with the final touring group of 24 due to be named next week, after Sunday's NRL Premiership final.
Meanwhile, Wests Tigers centre Tim Simona and Brisbane Broncos second row Alex Glenn have dropped out of contention through injury.
Kiwis train-on squad: Adam Blair, Lewis Brown, Greg Eastwood, James Fisher-Harris, Addin Fonua-Blake, David Fusitu'a, Shaun Johnson, Jordan Kahu, Solomone Kata, Shaun Kenny-Dowall, Thomas Leuluai, Isaac Liu, Tuimoala Lolohea, Issac Luke, Simon Mannering, Te Maire Martin, Suaia Matagi, Manu Ma'u, Sam Moa, Jason Nightingale, Jordan Rapana, Brad Takairangi, Joseph Tapine, Jason Taumalolo, Martin Taupau, Elijah Taylor, Jazz Tevaga, Bodene Thompson, Manu Vatuvei, Jared Waerea-Hargreaves, Dallin Watene-Zelezniak.