The Hijr is part of the House, because the Messenger of Allah ﷺ performed circumambulation around the House from behind it, and Allah said, "and let them circumambulate the Ancient House" [Hajj 22:29].
الحجر من البيت؛ لأن رسول الله ﷺ طاف بالبيت من ورائه، وقال الله: {وليطوفوا بالبيت العتيق}
Ibn Khuzayma (2740), Hakim (1/460), and Bayhaqi (5/90) all reported it through the route of Sufyan, from Hisham bin Hujayr, from Tawus, from Ibn Abbas, and mentioned it. Its chain is hasan because of Hisham bin Hujayr, for he is hasan al-hadith.It has also been narrated from Zuhri, from the Prophet ﷺ, that he said, "It is only called the Ancient House because no tyrant has ever prevailed over it." Tirmidhi (2137) reported it from Qutayba, who said, Layth narrated to us, from Aqeel, from Zuhri, from the Prophet ﷺ. The men of this chain are trustworthy, but it is mursal.Ibn Jareer Tabari likewise reported it in his Tafsir (16/531) through another route from Zuhri, who said, "It has reached us that the Messenger of Allah ﷺ said," and mentioned something similar.It has also been narrated as marfu. Tirmidhi (1370), Bazzar in his Musnad (2215), and Hakim (2/389) all reported it through the route of Abdullah bin Salih, who said, Layth narrated to me, from Abdul-Rahman bin Khalid, from Ibn Shihab, from Muhammad bin Urwa bin Zubayr, from Abdullah bin Zubayr, as marfu, with similar wording. This chain contains Abdullah bin Salih, who makes many mistakes, and this is one of the things he erred in.Mamar narrated it from Zuhri with the same wording as mawquf, stopping at Abdullah bin Zubayr, and this is the version that Abu Hatim judged to be correct. (Al-Ilal by Ibn Abu Hatim, 810).