The All Whites have been looking for a new manager since Ricki Herbert left his role in November.
Englishman Hudson is thought to figure highly on their wanted list after impressing since taking charge of Bahrain.
Hudson, son of former Chelsea star Alan, has been establishing a reputation as one of the best young coaches in the game and guided the country to their first ever under-23 title in the Gulf Cup of Nations before being handed the senior job last August.
The former West Ham trainee also became the youngest coach to take the UEFA and FIFA Pro Licences and his progress with the Bahrain national team has seen other countries take notice of his potential.
New Zealand are now weighing up a move for Hudson as they see the innovative and forward-thinking coach as the man who can take the country forward after they missed out on qualifying for this summer's World Cup finals.