During Arab occupationm. the jews were not allowed to pray there, it was used as a lavatories by the Muslims. The site has no significance for the Arabs. It belongs de jure to Jewish culture and de facto to Israel. The Muslims have Mecca, the Cristians Vatoican.
U.S. says working on initiative to de-escalate Syria fighting, with focus on Aleppo (Reuters)
from the article: U.S. condemns Palestinian claim that Western Wall 'isn't Jewish'