"It's not going to happen," Wallace told The Economist magazine in an interview, arguing that the United States wanted Stoltenberg to stay as secretary-general.
The UK government has been pushing its defence minister's candidacy after playing a lead role in providing Western arms to Ukraine to fight Russia's invasion.
But Wallace conceded that his bid had run afoul of the politics of the NATO role and the competing visions for the alliance of US President Joe Biden and French President Emmanuel Macron.
Stoltenberg's eventual successor "is going to have to please both Macron and Biden", he said in the interview, which was published online late on Wednesday.
Stoltenberg -- who has been at the helm of the Western military alliance since 2014 -- already had his tenure prolonged a year, to October, in the wake of Russia's invasion of Ukraine in February 2022.
Danish Prime Minister Mette Frederiksen has emerged as a possible frontrunner to succeed him, as NATO leaders prepare to hold a summit in Lithuania next month.
But there is so far no consensus on a clear pick among the 31 NATO countries, and diplomats are increasingly talking up the chances of Stoltenberg being asked to stay on.
The alliance faces strategic choices, as the United States corrals allies to get tough with China, while France pushes for greater self-reliance within Europe.
"The French have a point in lots of areas," Wallace said, highlighting the need for more collaboration among Europe's defence industries.
"The answer to everything is not America first, when it comes to procurement," he said.
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