"It's not going to happen," he told UK media answering a question about his plans to become the alliance's next secretary general, adding that the US wanted to extend Stoltenberg's mandate.
Wallace also suggested that Washington might want to see a prime minister as the new chief. The US has until recently favored Dutch Prime Minister Mark Rutte, but he has reportedly turned the job down several times.
However, sources close to Wallace reportedly say that the process remains open.
Media further added that the UK is facing an ammunition crisis. Wallace noted the Storm Shadow cruise missiles which had been sent to Ukraine had not been produced in the UK for 10 years, and that it took the country almost a year to restart supply chains for NLAW anti-tank weapons. The main problem is money, he told the outlet.
Wallace also supported France's position on NATO's expansion to the Indo-Pacific and opening an office in Tokyo, saying the alliance should not "mission-creep" there.
He added that the new chief "is going to have to please both [French President Emmanuel] Macron and [US President Joe] Biden."
Stoltenberg's term, who has led the alliance since October 2014, was scheduled to end on October 1 2022, but was extended until September 30, 2023.