This comes at a time when men have become more involved in some of Aware's activities, such as a campaign to end violence against women.
Currently, men can join Aware as associate members but they cannot vote at its general meetings or stand for election for any position on the board.
Aware president Teh Hooi Ling, in her first media interview since her appointment last month, told ST: "More men have become informed and have become our allies to achieve our common goal of gender equality."
One example is Aware's White Ribbon campaign, which raises awareness about violence against women, and emphasises the importance of men's role in ending it.
A campaign video last year featured 14 men, including Law Minister and Home Affairs Minister K. Shanmugam and actor Adrian Pang.
Said Ms Teh: "We will review our membership rules to see how we can accommodate both the needs of growing our male supporters, and maintaining Aware as a safe space for women."
She noted that Aware has to be safe for women who are abused or harassed, and for women to express themselves in ways that may be harder to do so in a male-dominated world.
An extraordinary general meeting is expected to be held by the year end to review the membership rules.
Read also: Aware turns 30
Former Nominated MP Siew Kum Hong, 41, decided not to renew his membership less than five years ago.
He disagreed with Aware's current position on membership rights for men.
He said of the upcoming review: "It's about time. I think it's reasonable to not grant equal rights to men, but the current balance is not right."
He said it would be fair if men could vote but not stand for election for certain board positions.
There are also strong male supporters of Aware, he added.
During the 2009 Aware saga, in which a group of mostly Christian newcomers swept the leadership team, he offered legal advice to the "old guard" group which regained control of the organisation five weeks after it was ousted.
Meanwhile, the Singapore Muslim Women's Association (PPIS) announced last week the appointment of its first male chief executive in 64 years, Mr Mohd Ali Mahmood.
PPIS said it believes his leadership will motivate more men to be part of the #heforshe movement, which is led by the United Nations and aims to get men to play their part in promoting gender equality.
Mr Mohd Ali said: "Problems affect everyone in the system, directly and indirectly.
"Men could be more involved in such conversations."
Singapore Council of Women's Organisations president Malathi Das agreed: "So long as the organisation and its members do not feel that having male membership or leadership in any way constrains its carrying out its mission and objectives, there should be no objection to including men in the organisation...
"We shouldn't throw the men out with the bathwater. Hearing their perspectives and ideas can also help in advancing the women's cause."
Read also: Gender equality still tops Aware's agenda
This article was first published on May 9, 2016.
Get a copy of The Straits Times or go to straitstimes.com for more stories.