The area from Hajar al-Aswad to the door of the Holy Ka‘bah is called the Multazam.[1] The literal meaning of the word Multazam is “the place to which one clings.” When the noble Companions came to Makkah, they would go to the Multazam, place their palms, arms, face and chest against it, and make du‘a. One may go to the Multazam and make du‘a before or after the Farewell Tawaf, or at any other time. Imam Ibn Taymiyyah (may Allah have mercy on him) said—
إن أحب أن يأتي الملتزم وهو ما بين الحجر الأسود والباب فيضع عليه صدره ووجهه وذراعيه وكفيه ويدعو، ويسأل الله تعالى حاجته، فعل ذلك وله أن يفعل قبل طواف الوداع ، فإن هذا الالتزام لا فرق بين أن يكون حال الوداع وغيره ، والصحابة كانوا يفعلون ذلك حين يدخلون مكة
—If one wishes to go to the Multazam—and the Multazam is the area between Hajar al-Aswad and the door—then one may place one’s chest, face, forearms and hands against it, make du‘a, and ask Allah for one’s needs; doing so is permissible. One may also do this before the Farewell Tawaf. There is no difference between doing this at the time of farewell and at other times. The Companions would do this when they entered Makkah.[2] However, in the present age, it is extremely difficult to reach the Multazam amid crowds of millions of people. Therefore, one should go if the opportunity arises; otherwise, there is no need to do so, because going to the Multazam is not part of Tawaf.
[1] Al-Musannaf li ‘Abd al-Razzaq: 5/73
[2] Majmu‘ al-Fatawa of Shaykh al-Islam Ibn Taymiyyah: 26/142