New Zealand Football are worried that pursuing their appeal against their disqualification from the Rio Olympics could open them up to further litigation.
Oceania Football disqualified New Zealand from the Olympic qualification tournament at the Pacific Games in Papua New Guinea in July, when they fielded South African-born defender Deklan Wynne.
New Zealand beat Vanuatu in the semi-finals and were set to play Fiji in the final for a place at Rio.
However Vanuatu lodged an appeal following their loss and were promoted to the final where they subsequently lost.
The next step was for NZF to take their appeal to the Court of Arbitration of Sport, which chief executive Andy Martin said they decided against.
"Whilst we got legal advice suggesting we could win this particular case on the one player with regards to the disqualification, there is a risk that could open up further action that is just not worth taking on."
New Zealand Football maintains its position that the action taken against one of its players and the subsequent disqualification of its Men's U-23 team from the Pacific Games was unfair.
Martin said New Zealand Football will now be seeking the support of the OFC and FIFA to change the current FIFA eligibility statutes and their application.
"We want to secure the opportunity for young people who have moved to New Zealand with their families as children and young adults for non-football reasons to play the game they love in New Zealand and represent their adopted country - something the statutes never intended to prevent," he said.