The next director of the Metropolitan Museum of Art is likely to be young, to have already run a museum — though not a major one — and to have a history of good relationships with curators. The next museum director sought by the Solomon R. Guggenheim Foundation is likely to have an international background and a track record as a fund-raiser and cost-cutter.

Not for a long time have two such powerful positions at New York museums been open at once, and, particularly now that the spring auctions are over, the art world can talk about little else. Both search committees are working as quietly as possible, but, as always, details trickle out.

Both museums are working with the search firm Phillips Oppenheim, but the jobs are different enough that there is supposedly little overlap in the candidates, with the possible exception of Michael Govan, who has been mentioned in connection with both posts. The searches are also at different stages. The Guggenheim’s search committee is conducting interviews, while the headhunters supposedly presented the Met’s committee with a list of names to consider only last week.

The Guggenheim’s committee, which is being run by the foundation’s chairman, William Mack, and president, Jennifer Stockman, is supposed to be talking to several candidates who currently work abroad, including the director of the Städel Museum and the Schirn Kunsthalle in Frankfurt, Max Hollein, and the American director of the Israel Museum, James Snyder. Although most directors of foreign institutions would not have the requisite fund-raising experience, these men have worked at New York museums — Mr. Hollein at the Guggenheim, where he was involved in setting up the branches in Berlin, Las Vegas, and Bilbao, and Mr. Snyder at the Museum of Modern Art, where he was a deputy director. Mr. Hollein’s office did not return a call from the Sun requesting an interview, and Mr. Snyder could not be reached by press time.

The Guggenheim is also rumored to be interested in Julián Zugazagoitia, who worked at the Guggenheim before becoming director of El Museo del Barrio in 2002. Mr. Zugazagoitia was born in Mexico City and graduated from the Sorbonne and the École du Louvre.

Asked if he had been approached about the Guggenheim job, Mr. Zugazagoitia said that “I formally have not had that conversation” with the search committee.

Meanwhile, the Met’s search committee, which is a mix of longtime board members, such as S. Parker Gilbert, Annette de la Renta, and Shelby White, and newer ones, has apparently taken several months to reach consensus about what it wants in a new director.

According to someone who had spoken with a committee member, the list that the search firm presented was young and, in general, surprising — including, among other names, that of the 56-year-old director of the Cleveland Museum of Art, Timothy Rub. (Mr. Rub’s office did not return a phone call.) The Met’s departing director, Philippe de Montebello, was only 42 when he was appointed to the position, and the search committee is rumored to be looking for another young director who can grow into the role.

Mr. Govan is young — in his mid-40s — but it is not clear whether he would be willing to leave his current job at the Los Angeles County Museum of Art. Some insiders suggest that Mr. Govan’s feelings about L.A. may have soured since Eli Broad announced, earlier this year, that he would not leave his art collection to LACMA, but only loan pieces for exhibition. Mr. Govan did not return an e-mail yesterday.

Another question mark is the director of the Art Institute of Chicago, James Cuno. Mr. Cuno recently published a book, “Who Owns Antiquity?,” in which he criticized cultural property laws and defended encyclopedic museums. Many in the art world interpreted the book as a memo to the Met’s search committee. But Mr. Cuno told the New York Times, and said again in an interview with the Sun, that he hasn’t been contacted by the Met.

Last but not least is the Met’s internal candidate, Gary Tinterow, currently the curator in charge of 19th-century, modern, and contemporary art. Choosing Mr. Tinterow would represent a decision to significantly expand the Met’s involvement with contemporary art, which he has championed. Since he has not previously run a museum, his accession to director might also mean a greater delegation of administrative responsibility to the Met’s seasoned president, Emily Rafferty.

The press offices of the Met and the Guggenheim did not return e-mails last evening. The partners at Phillips Oppenheim who are running both searches, Sarah James and Laurie Nash, declined to comment on their progress.