Lawrence Summers still has a month left as president of Harvard University but already there is extensive guesswork going on in Cambridge and beyond about who will replace him.

Faculty buzz mostly centres on possible in-house candidates - several of whom are women - or the potential for a "marquee" political figure, such as Al Gore or Condoleezza Rice, taking the job. But this, of course, is all merely conjecture. This search will be nothing if not secretive.

"Leadership transitions have all the interest of a wake, a birth and a wedding all rolled into one," says Judith McLaughlin, a professor of higher education at Harvard and an expert on college presidential searches. "They are exciting moments in an institution's life and there's great curiosity and speculation about it."

The ultimate choice remains with the corporation, the university's governing board. At the end of March, the corporation named a nine-member search committee, including six of the seven corporation members; Mr Summers is the seventh. The others come from the university's board of overseers - two are academics and the third is a lawyer in Boston.

Traditionally, Harvard's presidential searches have been top-down, high-level affairs, but this time - perhaps because faculty opposition forced Mr Summers out - Harvard appears to be making conciliatory overtures. It is in the process of creating faculty and student advisory groups to help in the search.

As with the last search, which ended with Mr Summers's selection, Harvard has already begun with a broad appeal for input. It has created an e-mail account to receive nominations and has sent letters to all faculty, students, staff, donors and alumni seeking their views.

Harvard's last presidential search took eight months from its official launch, in July 2000, to Mr Summers's acceptance of the job in March 2001. While the corporation will not set a specific date for hiring his replacement, in order to avoid criticism if the search takes longer than expected, officials say they are hoping to finish in nine to 12 months.

Joe McCabe, managing partner with Heidrick and Struggles, the recruitment firm that recently conducted academic searches at Cambridge and the University of North Carolina at Charlotte, says the university may look to hire its first woman president. "We see this all the time in clients across the board," he says. "For senior leadership roles, institutions want a search removed from the old boy network and they want to have diversity on the roster."

In recent years many US universities have selected women leaders. Brown University hired Ruth Simmons in 2000, and in 2004, the Massachusetts Institute of Technology appointed Susan Hockfield and the University of Pennsylvania made Amy Gutmann president.

Morton Keller, a historian and co-author of Making Harvard Modern: The Rise of America's University, predicts that the corporation will choose a Harvard insider. "Clear candidates haven't emerged but there will be a strong inclination to appoint an insider," he says. "The more continuity the better."

Inside candidates in the mix include two women: Drew Gilpin Faust, dean of the Radcliffe Institute for Advanced Study, and Elena Kagan, dean of the law school, as well as Steven Hyman, provost of the university. Nannerl Keohane, former president at Duke University and Wellesley College and a member of Harvard's corporation, was thought a potential candidate until she took herself out of the running in March.

There are prominent candidates outside the university too. Lee Bollinger, the president of Columbia University who was a finalist in the last Harvard search, has been mentioned again, as has Ms Gutmann at Penn.

Many on the faculty have expressed wariness at the prospect of another outside candidate from Washington - Mr Summers served as Treasury secretary under President Bill Clinton. "I hope that the next president will not be from Washington," says Harry Lewis, professor of computer science and former dean of the college. "One of Larry's problems was that he worked on a congressional election timetable and so everything had to get done within a year."

Mr Keller, the historian, adds that the corporation will be especially looking for someone with a softer demeanour than Mr Summers, whose outspoken views and abrasive managerial style made it difficult for him to connect with a substantial portion of Harvard's faculty. "It would seem that the time is right not for someone who is going to turn everything upside down but an emollient consolidator who will be a quieting force," says Mr Keller.

But, says Henry Rosovsky, a former corporation member who has chaired past Harvard searches, all this chatter about what the corporation is looking for is merely speculation. "In my experience, these things come down in the end not to theories about the kind of people you want, but people. It comes down to the choice of a person," he says.