The All Blacks are on the hunt for a new head coach following the end of Steve Hansen's reign, which returned two Rugby World Cup triumphs and a run to the semi-finals of this year's tournament in Japan.
Gatland also ended his 12-year reign with Wales after the World Cup and was tipped as potential successor to Hansen.
However, the 56-year-old had already signed a four-year deal with Super Rugby side Chiefs, during which time he will take a year out to coach the British and Irish Lions for a third time.
Gatland said the timing of the All Blacks opportunity was not right but discussions with New Zealand's high performance manager Mark Anthony left the door ajar in future.
Asked if he would still like to coach New Zealand, Gatland told The Guardian: "Absolutely.
"I went back and gave my reasons why I just couldn't apply for the job right now. I've got it on my phone."
Gatland fell agonisingly short of ending his Wales tenure with at least an appearance in the World Cup final as his side went down 19-16 to champions South Africa in a tense last-four clash.
Had Wales found a way past the Springboks, Gatland is convinced Wales could have beaten England in the final.
"I thought if we beat South Africa, even with injuries, I would've gone into the game against England feeling we could win the World Cup," he said.
"There wasn't that fear factor against England. It would have been different if the All Blacks had won their semi-final. For some of the Welsh players the All Blacks are still on a pedestal because New Zealand’s the one team we haven't beaten.
"But against England, psychologically, we would have been confident because the guys have had success and we had an effective game plan.
"The results have been 50-50 and, knowing you're capable of beating them, makes a massive difference."
England's own place in the final was booked with a barnstorming victory over New Zealand, a performance Gatland opined would be difficult to replicate.
That drew a retort from Eddie Jones that Gatland should enjoy the third-place play-off fixture.
But Gatland said the comments from both men were not said with hostility.
"I wasn't actually referring to England," Gatland said. "And Eddie wasn't being malicious in his comment.
"Eddie and I often laugh about this because it's a game. What I meant is that if you look at previous World Cups the only team that has beaten the All Blacks and gone on to win it is Australia.
"Emotion plays a massive part in big games. It's very difficult, at the highest level of sport, to be right on the edge emotionally and repeat that the following week."