The Rugby League International Federation's (RLIF) executive committee held a conference call Tuesday and gave New Zealand until the following day to put its case before announcing a ruling on Thursday.
The RLIF said in a statement it would determine "any possible consequences" if it was found 27-year-old Australian-born Nathan Fien was ineligible to play for New Zealand.
The loss of competition points is one of the penalties the RLIF could impose, but if it viewed the rules breach less seriously, a fine could be imposed.
The controversy erupted after an admission by the New Zealand Rugby League (NZRL) that the former Queensland State of Origin player was selected for the Kiwis on the basis of having a New Zealand-born great-grandmother.
The rules allow for a player to be selected for a country provided they have a grandparent born there.
Fien, who plays at hooker for the New Zealand Warriors, appeared for the Kiwis as a substitute in their 20-5 loss against Australia and started in the 18-14 victory over Great Britain on Saturday.
NZRL chairman Selwyn Bennett earlier threatened the Kiwis would boycott the second Test against Great Britain -- scheduled for Wellington on November 11 -- if they were stripped of their points from Saturday's win.
But Bennett withdrew the threat Wednesday.
"It's very emotional and you do say things on the spur of the moment," Bennett said on Radio New Zealand.
"You get very heated when they threaten your team, the Kiwis are our national team, and I'll defend them to the end."
The Kiwis face a much tougher road to the final of the series if stripped of the winning points after losing both Tests against Australia. Each team play each other twice before the two top teams go through to the final.