“She feels like she’s been treated very well in the way she’s been asked,” said a close associate of Mrs. Clinton, who like others interviewed asked for anonymity because the nomination will not be formally announced until after Thanksgiving.

Image President Bush and Colin L. Powell had a strained relationship. Credit... Doug Mills/The New York Times

Few are predicting that this new relationship born of mutual respect and self-interest will grow into a tight bond between the new president and the woman who will be the public face of his foreign policy, though some say it is not impossible. They argue that a close friendship between the two powerful officials is useful but not essential, and is not a predictor of the success of the nation’s chief diplomat.

While James A. Baker III was extraordinarily close to the first President George Bush and is widely considered one of the most successful recent secretaries of state, Dean Acheson was not a friend of Harry S. Truman and Henry A. Kissinger did not particularly like Richard M. Nixon.

“Two of the nation’s greatest secretaries of state in the modern period, Dean Acheson and Henry Kissinger, were not personally close but were intellectually bonded to their presidents,” said Walter Isaacson, the author of a biography of Mr. Kissinger and the co-author, with Evan Thomas, of “The Wise Men,” a book about America’s postwar foreign policy establishment. “I think that Obama and Clinton could form a perfect partnership based on respect for each other’s view of the world.”

Colin L. Powell, who was President Bush’s first-term celebrity secretary of state, would appear to be a cautionary tale for Mrs. Clinton since his relationship with the president was strained, and he left office an unhappy man. But Mr. Bush’s second-term secretary of state, Condoleezza Rice, is generally not viewed as having the success her unusually tight bond with the president might have engendered.