Wallace, 53, is considering whether to stand down from government after four years as defense secretary.
Wallace could leave the government during the reshuffle that UK Prime Minister Rishi Sunak is planning this fall, the publication specified.
Possible candidates for the post of UK defense secretary include Chief Secretary to the Treasury John Glen, Minister of State for Security Tom Tugendhat and Anne-Marie Trevelyan, the United Kingdom's Minister of State for the Indo-Pacific.