The mosque's president, Shafi Kausar, said female worshippers were now being encouraged to apply for place on the giant Clydeside complex's management committee.
This comes after years of women claiming they were being told they could not join for a variety of reason, including the need for "ladies" to be chaperoned by male relatives at meetings.
A new mosque committee was due to be elected on Sunday evening. However, Dr Kausar, speaking to The Herald before the meeting, said: "We want more women to apply. We are going to extend the deadline for them so that if they want to apply, the can. I would have no problem with women. We need them."
The Mosque veteran said there had been 68 applications for places on the management committee but only one from a women, a relative of an existing member.
Dr Kausar said regular female worshippers - who pray separate from men - had not come forward.
He added: "The women who go to the mosque do not want to go on the committee because they know they are doing all right. They have their own committee."
The new stance on female membership comes after months of pressure on Glasgow Central Mosque to widen access to its ruling committee to both women and non-Pakistanis.
Women rarely get to positions of power in British Mosques, which tend to be dominated by men of Pakistani origin. There is no religious reason why females should not take part in committees managing the finances and housekeeping of mosques.
Some liberal Mosque insiders are sceptical about the announcement on women, suggesting it was a "grand gesture" rather than a serious policy. One said: "We shall see if any women members actually materialise."
Another source suggested it was a "delaying tactic" and had more to do with internal mosque politics than big gender issues.
Women who have previously expressed an interest in joining the committee have insisted that lack of a "mehram" or chaperone was a stumbling block. One female source said: "Most of those justifying this exclusion work in professions which require them to work with non-mehram women.
"Moreover, committee meetings are group meetings not one to one meetings."
A male liberal said: "This is just hypocrisy. These guys are quite happy sitting down with Nicola Sturgeon when she hasn't got a chaperone."
The latest gambit at the Mosque came as a conference began at Glasgow University focusing on gender issues in Islam. One speaker, Glasgow-born academic Dr Amanullah De Sondy, writing in The Herald, said: "What we see today is the visibility of different voices within Muslim communities that have often been invisible.
"The heterosexual, male dominated hierarchy is being challenged by voices from the margins from women and those from the LGBT communities. These voices make up the beautiful colours of the tartan of Islam that Muslims need to appreciate even if they disagree with them."
The Herald understands at least one white convert has applied to be on the board and that there have been tentative talks with both Arabs and Somalis about their role at the Mosque.
Orthodox Pakistanis have been in firmly control of Glasgow Central Mosque since earlier this spring when liberal resigned, citing intimidation.
Scotland's charity watchdog is engaged in a long-standing investigation in to the Mosque, including the contact of its real power base, the "property trustees" who sit above the management commttee.