Al-Bayhaqī narrated it. However, ʿAlī ibn ʿĀṣim is somewhat weak, and ʿAbd al-Razzāq contradicted him, reporting (9044): Ibn Jurayj said: ʿAmr ibn Shuʿayb said: “Muḥammad—his grandfather—circumambulated the House with his father, ʿAbd Allāh ibn ʿAmr...” and he related something similar. Ibn Jurayj practised tadlīs, and it is possible that the intermediary between him and ʿAmr ibn Saʿīd was al-Muthannā himself. Thus, the hadith is not strengthened by his route from ʿAmr, especially in view of this discrepancy in its chain from him.
It is, however, supported by what Yazīd ibn Abī Ziyād narrated from Mujāhid, from ʿAbd al-Raḥmān ibn Ṣafwān, who said: “When the Messenger of Allah, peace and blessings be upon him, conquered Mecca, I said, ‘... I shall certainly see what the Messenger of Allah, peace and blessings be upon him, does.’ So I went out and saw that the Prophet, peace and blessings be upon him, had come out of the Kaʿbah along with his Companions. They had touched the House from the door to al-Ḥaṭīm, and had placed their cheeks against the House, while the Messenger of Allah, peace and blessings be upon him, was in their midst.” It was narrated by Abū Dāwūd, al-Bayhaqī, Aḥmad (3/431), and also by Ibn Abī Shaybah in his Musnad (2/35/2). Its narrators are trustworthy, except for this Yazīd—al-Hāshimī, their freedman—whose retention was weak.
I found for it a strong corroborating report attributed to a Companion. ʿAbd al-Razzāq narrated (9047): from Ibn ʿUyaynah, from ʿAbd al-Karīm al-Jazarī, from Mujāhid, who said: Ibn ʿAbbās said: “This is the Multazam: the space between the Corner and the door.” I say: This is an authentic chain. He then narrated from Hishām ibn ʿUrwah, from his father, “that he would press his chest, hand, and abdomen against the House.”