The deadline for applications passed on Wednesday evening and Mallinder has revealed he was not among those to apply for the position.
Mallinder, who previously coached England U21s and Saxons, had been among the favourites to become Martin Johnson's long-term successor.
"No, I've not applied," Mallinder told the BBC. "It's probably the best job in the world coaching wise. What a great opportunity. But it's got to be the right thing at the right time.
"At the moment I'm concerned with getting Northampton to win something.
"I spoke to [Rugby Football Union director of operations] Rob Andrew a month or so ago. As I have done previously, I expressed that one day I think it's a tremendous job to do."
Wayne Smith, who was part of the All Blacks' World Cup winning coaching team, has also ruled himself out of the running.
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