The pounds 43,500 post, which supporters believe could become one of the most high-profile positions in British feminism, has just been advertised.
Construction work on the pounds 7m library begins this month on the site of a former Victorian wash-house in Aldgate, east London.
It will be the first purpose-built home for a collection started by the Fawcett Society equality campaign group in 1926 and housed in a cramped basement at the London Guildhall University since the 1970s.
Maureen Castens, the university's academic services director, who had the idea for the building six years ago, said: "We want somebody who has a very clear vision for this."
Ms Castens said some argued that at the end of the 1990s society had been feminised and there was no need for a library dedicated to women. But she believes the fact that she is constantly forced to defend the project explains the need.
"Look at the Suffrage movement - that wonderful belief that if women could get into public life and could vote that the world would change. Of course, it's not quite like that."
Asked whether she thought a man could get the job, Ms Castens said: "I think we've got an awful lot of exceptional women around in this country. If there's a super-exceptional man out there who can make the case he's welcome to apply."
Betty Boothroyd, the House of Commons' Speaker, is the scheme's patron and Labour MP Barbara Follett heads the fund-raising steering committee.
The Heritage Lottery Fund gave pounds 4.2m and other funding has come from bodies including the Higher Education Funding Council for England.
Another pounds 1.3m is needed for the capital programme with a further pounds 4m for an endowment fund to run the library, which is being designed to environmentally friendly standards. There will be conference facilities, a shop and a cafe.
The existing Fawcett collection consists of about 60,000 books and pamphlets and more than 2,000 journals. It includes material from the 19th century and banners from the early years of the Suffrage movement. Many of the books were either donated or paid for by the writer Virginia Woolf.
A similar collection was begun at Harvard University 20 years ago charting the American feminist struggle. Ms Castens said that when she visited it, she realised that the Fawcett library was at least as important.
Jane Grant, an executive committee member of the Fawcett Society, is completing a doctorate on women's organisations which has been researched largely through the collection.
She said the existing storage was inhospitable. "It is great cause for celebration that there is going to be space, not just to house what's already there, but to attract in other collections."
Ms Grant said some people now understood that what was once considered neutral history was, in fact, almost entirely a male history.
"But the idea is far from universally accepted. Many people, I dare say, would laugh at the concept, but having such a high profile building will make them less inclined to do so."