Wallace, a former captain in the British Army, is seen as a leading contender to replace Jens Stoltenberg who will retire as NATO secretary-general in October after two terms.
Sunak is reportedly set to personally lobby US President Joe Biden to back Wallace for the role, during a visit to Washington Wednesday and Thursday.
The United States is the dominant force within the 31-member military alliance, and its endorsement is crucial for whoever takes the top job.
Asked whether he would push in Washington for Wallace's appointment, Sunak did not directly answer but heaped praise on his 53-year-old cabinet colleague.
"Ben does a fantastic job. He is a great defence secretary," he told reporters, noting that conversations around the NATO role were "happening amongst leaders".
"Ben is widely respected among his colleagues around the world," he added, before detailing Britain's prominent role within the military alliance.
Wallace has travelled widely as defence secretary and enjoys an easy rapport in public with US officials, after taking a prominent role responding to the war in Ukraine.
Last month he appeared to show an interest in the NATO post, telling German news agency DPA that it's "a job I'd like".
Denmark's Prime Minister Mette Frederiksen -- who meets Biden in Washington on Monday -- is also thought to be in the running, and would become NATO's first woman chief if chosen.
But eastern European countries have never been represented in the top job, and are lobbying for one of their own to take the NATO helm.
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