Upon hearing the news the NFF stated its intention to contact FIFA over the situation in the same way Senegal did when Papiss Cissé failed to attend a friendly, with the striker consequently forced to miss the home game with Swansea in November.
Speaking on the matter, NFF board member Chris Green wished Ameobi and Millwall's Danny Shittu the best following their decision to opt out.
"We have decided to focus our energy on the players and officials going to the Nations Cup in South Africa," he said. "There's no point creating unnecessary distraction or pushing for sanctions when we have capable players in the Super Eagles.
"We have the rules firmly on our side to seek punishment but that will not make any positive contribution to our preparations. There are players in the squad who can deliver for Nigeria, so we can only wish Ameobi and Shittu all the best in England."
The news will come as a welcome boost to Pardew, who revealed after the club's 1-0 home win against Queens Park Rangers in December that he did not expect Ameobi to attend the tournament.
Despite the news, the striker will still miss this weekend's game against Norwich City through suspension after being dismissed in the 2-0 FA Cup defeat at Brighton last weekend. He will instead return for Newcastle's next home game against Reading in just under a fortnight's time.