Ben Zion Luria believes that had Herod been the sponsor of the Haram, Josephus would undoubtedly have described the edifice—as he had described construction of other important Herodian projects. But Josephus is notably silent with respect to the Hebron Haram. (See “The Edifice Of Maarat Machpelah and Its Date,” Sefer Hevron, pp. 273ff (in Hebrew).)