I am not saying it is going to happen. It probably never will but it is not as unlikely as you might think. Read this article from Touchstone on the subject.
Some excerpts :
A large ( unofficial) conference issued this statement :
There are no binding dogmatic reasons present against the admission of women to priestly service.
The article looks at editor Thomas Hopko's 1999 book on the subject and notes the shifting attitudes in Orthodoxy on women in the priesthood. The new edition of the book differs significantly from the first edition in 1983. There is a sizable group in EO who are open to the women priests and who are exploring the patristic and theological possiblity for such a claim. Sister Nonna Harrison
finds the “argument that men should hold all leadership positions in Church, family and society particularly disturbing.” In the Fathers, she writes, the divine nature is devoid of gender, and conceived in wholly apophatic terms. On the human plane, however, “the ideal is whole and abundant life” rather than the “androgyny” in modern ideologies, which reduces men and women to lowest common denominators. The goal is a development of positive human qualities in the pursuit of holiness, many of which will make “women in the end acquire masculine virtues, as well as feminine ones,” and vice versa.
The article relates the startling fact that women deaconesses have been administering Holy Communion to other women:
Most recently, Metropolitan Christodoulos of Dimitriados “appointed the abbess of the women’s monastery of St. Spiridonos Promiriou as a deaconess” in 1986. She was charged with administering Holy Communion to the nuns when needed, and the action was clearly based on the earlier one of St. Nektarios. This account was of course not present in the 1983 edition.
Kallistos Ware has to have become much more open to the ordination of women without actually advocating for it:
“My views on the issue have altered,” he writes.
In 1978 I considered the ordination of women priests to be an impossibility. Now I am much more hesitant. I am far from convinced by many of the current arguments in favor of women priests; but at the same time a number of the arguments urged on the other side now appear to me a great deal less conclusive than they did twenty years ago ...
He outlines three questions of “crucial importance”: The first is about “the nature and authority of Tradition”; the second deals with anthropology, and how far we can attach “theological significance” to distinctions between men and women; and the third is about the precise meaning of priesthood, and the significance in that definition of Christ’s own maleness as opposed to his humanity.
On all three of these matters Bishop Kallistos offers interesting and sometimes surprising reflections, admitting that their full implications have not yet been examined by the Church as a whole. On the nature of the priesthood, for instance, he writes that “at no point in the actual prayer of consecration does [the priest] speak in persona Christi.” Rather, the Orthodox priest speaks during the Anaphora “in persona Ecclesiae, as the representative not of Christ but of the Church.” As a result, the “iconic argument against the ordination of women is bound to seem less conclusive to Orthodox Christians than it does to Roman Catholics.”