Kiwi fans were dealt a blow when Blatter announced after his re-election that the current allocation of World Cup confederation slots would remain in place for the next two tournaments in 2018 and 2022.
This meant the OFC, largely dominated by the All Whites, would still have a half spot, and would still need to qualify via an inter-continental playoff.
Mr Martin said "all bets are off now" as Blatter's resignation had given NZ Football a chance to re-open dialogue with new Fifa leaders.
He said although it might be too late for the 2018 World Cup, the 2022 tournament was still far enough away to try to change the decision.
"I think certainly all of the new candidates are going to want to come and talk to us and we've made our position very clear on what we think going forward."
Mr Martin said there were a number of options to now consider, including aligning closer to Asia, or "re-cutting" the confederation.
"Right now, having a play-off game against a random team from one of the other confederations, and coming up with a team like Mexico, just doesn't feel right or fair in terms of giving us a shot at getting to the World Cup."
He said New Zealand did not want a "gifted place" at the Cup.
"The most important thing for New Zealand football is competitive football on a regular basis."
Mr Martin said the resignation was unlikely to affect the Fifa U-20 World Cup being played in New Zealand.
The chief executive of the tournament's local organising committee, Dave Beeche, recognised the developments in Zurich as "significant" and said the committee fully appreciated the "big impact" it would have on the world of football.
"However, we have a significant job to do right here in New Zealand to ensure that the biggest football event ever staged in this country is a success and we continue to work closely with our colleagues from Fifa, who are here in New Zealand to ensure that this happens."
He could not say if Blatter's planned trip to NZ had been cancelled. "It was always his intention to come to New Zealand nearer the end of the tournament but we are yet to receive any official confirmation."
Meanwhile, the organisation NewFifaNow - which includes parliamentarians, formal football officials, people from the corporate sector and supporters and players' groups - has put forward some well-known names to lead "a short-term independent reform commission to completely transform the governance of world football".
One of the names mentioned is former New Zealand Prime Minister Helen Clark, now head of the United Nations Development Programme.
