The Auatralian coach has made his frustrations over the perceived eligibility problems in the international game clear in recent times.
Losing Brian To'o to Samoa already, a whole host of players could yet defect away from the Kangaroos in the coming weeks, with Meninga wanting all players to make their mind up before he names his training squad.
The blow on Kaufusi - who played Game 1 and 2 of the recent State of Origin series, but missed Game 3 due to personal circumstances - will come as a bitter one for the Kangaroos.
News Corp are reporting the Melbourne Storm, but Dolphins'-bound veteran forward has only made his decision this week, but has ultimately committed to join the Tongan cause.
He would likely have been a walk up selection in the Australian squad, with Cameron Murray a likely selection on the other end amid a dearth of suitable back row options for Meninga and a yet to be confirmed selection panel, with both Brad Fittler and Billy Slater reportedly opting out.
The 30-year-old has played 165 games for the Melbourne Storm since debuting in 2014 and 14 games for Queensland in the Origin arena, and would have brought much needed experience to the Kangaroos' squad.
Instead, he will take his talents to Tonga, where he will be joined by the likes of Jason Taumalolo, Addin Fonua-Blake, Kotoni Staggs and Tesi Niu among others who all played for the nation in the recent representative round against New Zealand.
A host of other players are yet to commit either way, with Jarome Luai and Stephen Crichton seemingly likely to follow Penrith teammate To'o, while Tino Fa'asuamaleaui, Jeremiah Nanai, Josh Papali'i and Junior Paulo out of the Origin squads could also move out of the Australian set up.
The World Cup will played in England during October and November.