Harvard and Princeton universities have traditionally competed for students. But now the two schools are both looking for new presidents and may be wading in the same talent pool.

Former Princeton dean Amy Gutmann is the newest candidate on Harvard’s short list for president, the Daily Princetonian reported. Officials said both schools are likely drawing candidates from the same list, but differences in their size and makeup will inhibit significant overlap in their searches.

Last week, the Daily Princetonian reported Harvard may reach into Princeton for its next president, since Gutmann met with the Harvard presidential search committee for the second time in New York two weeks ago. She joins the ranks of former U.S. Treasury Secretary Lawrence Summers, Harvard Provost Harvey Fineberg and University of Michigan President Lee Bollinger — the short list for the Harvard replacement as reported by the Boston Globe and the Harvard Crimson.

Sources close to Gutmann said they believe it is likely the Princeton presidential search committee is also considering her to fill president Harold Shapiro’s seat.

“She must be a candidate for Princeton president,” said David Wilkins, a Harvard Law School professor and close friend to Gutmann. “She is very well regarded and has spent more than 20 years of her career there.”

At both universities, trustees are conducting the entire search processes, which are confidential. No specific names on the Princeton short list for president have been reported. Princeton politics professor George Kateb described his school’s search process as “leak proof.”

Harvard began its search to replace president Neil Rudenstine in May 2000 when he announced he would end his 10-year tenure this spring. And in late September, Princeton’s Shapiro announced he too would resign at the end of this academic year.

While both schools are prestigious research universities, officials said differences between the two schools will likely propel them to seek out different types of leaders.

“Princeton needs a president that will focus on the undergraduate and arts and sciences,” Kateb said. “Harvard has many more students and needs someone to focus also on the many professional schools.”

The differences between Harvard and Princeton are significant. Princeton has 6,000 students at the undergraduate and professional level while Harvard has more than 15,000 total students and places a greater emphasis on graduate education. Harvard, like Yale, has medical, law and business schools.

But Wilkins said in general, both schools are looking for leaders who meet the same criteria.

“Both schools are looking for someone of academic distinction that are also good managers,” Wilkins said. He added that for Harvard, the leadership skills are more important than for Princeton because the Crimson have a “complex bureaucracy.”

Provost Alison Richard, Yale’s chief academic and financial officer, said the challenges for Harvard and Princeton are to secure leaders whose qualities are the right match for this moment in the school’s history.

“Different institutions weigh different aspects of people’s candidacies,” Richard said. “Trustees may judge that particular character traits are suited to the moment.”

Last November, Brown University narrowed the talent pool for both schools when it named former Smith College chief Ruth J. Simmons as its new president. The Harvard Crimson and the Daily Princetonian reported Simmons had been a candidate for president at both schools.