The Gunners had targeted the Colombian defender, as he is out of contract with the Serie A club in the summer.
Although it now appears new Napoli boss Rafael Benitez has persuaded Zuniga to sign a new deal at the club, with reports suggesting the deal will include a clause that could see the defender join Barcelona in the future.
Arsenal have not been the only club linked with the highly rated defender.
Italian giants Juventus and Inter Milan have both been monitoring his situation closely, whilst Barcelona are also said to have shown an interest.
Reports in Italy have suggested Zuniga has been unwilling to extend his contract at Napoli in the hope the Catalan giants will make a cut price offer for his services in January.
However it now appears likely he will sign a contract extension on the condition he can move to Barcelona should the Spanish champions make an offer of £12.5million at any point over the next five years.
The news will come as a blow to Arsene Wenger, who had earmarked Zuniga as a top target due to his ability and the fact he would have been relatively cheap considering his contract situation.
The Gunners boss has been told he will have money to spend in January, and has made a new centre back and a new striker his top priorities.