The HC had held that the trust had no power to alter or modify the mode or manner of religious practices of any individual or any group.
On August 26, the Bombay HC had lifted the ban imposed on women from entering the inner sanctum of Mumbai's Haji Ali Dargah.
Migrants hailing from Gonda, Ambedkar Nagar, Unnao and other parts in Uttar Pradesh were looking forward to reach their homes.
The judges said both the matters were similar involving entry of women in the religious shrines, and hence they would like to see what view would Supreme Court take on the issue before they give a ruling on the interim relief sought by the petitioner in the Bombay high court.
Haji Arafat said that the attempt by Desai to enter the Haji Ali Dargah is a conspiracy meant to disturb Mumbai's peaceful environment.
Maharashtra government on Tuesday favoured entry of women in the sanctum sanctorum of the renowned Haji Ali Dargah in Mumbai.
The entry by members of Bharatiya Muslim Mahila Andolan into the mausoleum came more than a month after the Haji Ali Dargah Trust told the Supreme Court it will allow women inside the inner sanctum of the shrine. Women devotees' entry into it was banned a few years ago.
Several activists belonging to Muslim women groups held placards demanding entry for females into the sanctum sanctorum of the historic dargah, which receives hundreds of devotees everyday.