What is the ruling on praying the two rak‘ahs following tawaf outside the mataf area?
Question

Is it permissible to pray the two rak‘ahs following tawaf [circumambulation of the Ka‘bah] outside the mataf [area surrounding the Ka‘bah where tawaf is done]?
Praise be to Allah.It is Sunnah to pray two rak‘ahs following any tawaf, and it is mustahabb [recommended] to do that behind Maqam Ibrahim [the Station of Abraham].
Al-Bukhari (1627) and Muslim (1234) narrated that Ibn ‘Umar (may Allah be pleased with him) said: The Prophet (blessings and peace of Allah be upon him) came and circumambulated the House seven times and prayed two rak‘ahs behind the Maqam, then he went out to as-Safa; and Allah, may He be exalted, says (interpretation of the meaning): {Verily, in the Messenger of Allah you have a good example} [al-Ahzab 33:21]. It is permissible to pray these two rak‘ahs anywhere in the mosque, or in Makkah and the Haram zone.
Imam Malik narrated in al-Muwatta’ (1/368) from Humayd ibn ‘Abd ar-Rahman ibn ‘Awf that ‘Abd ar-Rahman ibn ‘Abd al-Qari’ told him that he circumambulated the Ka‘bah with ‘Umar ibn al-Khattab after Fajr prayer. When ‘Umar had finished his tawaf, he looked around and saw that the sun had not risen, so he rode his mount until he halted in Dhu Tuwa, where he prayed two rak‘ahs.
Ibn al-Mundhir (may Allah have mercy on him) said: It is soundly narrated that the Messenger of Allah (blessings and peace of Allah be upon him) circumambulated the Ka‘bah, then he prayed two rak‘ahs at the Maqam.
The scholars are unanimously agreed that wherever the one who has completed tawaf prays the two rak‘ahs following tawaf, it is acceptable, apart from Malik, who regarded it as makruh (disliked) to pray the two tak‘ahs following tawaf in the Hijr [semi-circular area next to the Ka‘bah]. End quote from al-Ishraf (3/287).
Ibn Qudamah (may Allah have mercy on him) said: It is Sunnah for the one who has completed tawaf to pray two rak‘ahs after completing it, and it is recommended to offer this prayer behind the Maqam, because Allah, may He be exalted, says (interpretation of the meaning): {Take the Station of Ibrahim as a place of prayer} [al-Baqarah 2:125].
Wherever he prays these two rak‘ahs and whatever he recites in them, it is permissible, as ‘Umar prayed them in Dhu Tuwa."(Al-Mughni  3/347).
Shaykh Ibn Baz (may Allah have mercy on him) said: It is not obligatory for the one who has completed tawaf to pray the two rak‘ahs behind Maqam Ibrahim. Rather it is prescribed for him to do that if he is able to do it without difficulty, but if he prays them anywhere in al-Masjid al-Haram or in any place in the entire Haram zone, that is acceptable.
It is not prescribed for him to push and shove with those who are still circumambulating in order to pray these two rak‘ahs at the Maqam. Rather he should keep away from the crowds and pray them in another part of al-Masjid al-Haram, because on one occasion ‘Umar (may Allah be pleased with him) prayed the two rak‘ahs following tawaf in Dhu Tuwa, which is part of the Haram zone, but it is outside al-Masjid al-Haram. Umm Salamah (may Allah be pleased with her) also prayed the two rak‘ahs following tawaf outside al-Masjid al-Haram. What appears to be the case is that the reason she did that was because of the crowds, or because by doing that, she intended to demonstrate to the people how flexible this matter is according to Islamic teachings."(Fatawa Ibn Baz 17/228).
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said: Those who pray behind the Maqam and insist on praying there, when those who are circumambulating the Ka‘bah need the space, are wronging themselves and wronging others. They are sinning, transgressing and doing wrong. They have no right to this space, and you have the right to push them away, you have the right to walk in front of them, and you have the right to step over them when they are prostrating, because they have no right to this space at all.
The fact that they insist on being in that place is undoubtedly due to their ignorance, because the two rak‘ahs following tawaf may be done in any part of the mosque. A person can move away from the place where people are circumambulating and pray two rak‘ahs. The caliph ‘Umar ibn al-Khattab (may Allah be pleased with him) even prayed the two rak‘ahs following tawaf in Dhu Tuwa, which is far away from al-Masjid al-Haram, and is not even part of it.
The individual must fear Allah regarding himself and fear Allah regarding his brothers. So he should not pray behind Maqam Ibrahim when people need that space for tawaf. He has no protection [in this case, according to Islamic teachings] and we have the right to push him, we have the right to interrupt his prayer, and we have the right to step over him when he is prostrating, because he is the one who is transgressing and doing wrong – Allah forbid."(Fatawa ‘Ulama’ al-Balad al-Haram  p. 220).
Conclusion:
It is permissible to pray the two rak‘ahs following tawaf in any place in Makkah and the Haram zone. The best is to pray them behind Maqam Ibrahim, if there are no crowds and you will not cause any obstruction or make it difficult for those who are circumambulating the Ka‘bah by praying behind Maqam Ibrahim.
And Allah knows best.