“My impression is, because I know some of the people and friends around Donald Trump, I believe that it will happen, sooner rather than later,” he said.

Mr. Barkat’s optimism partly reflects a broad confidence expressed by Israel’s top leaders that they will have a much closer relationship with the Trump administration than they had with its predecessor.

Prime Minister Benjamin Netanyahu of Israel said as much in a “60 Minutes” interview recorded for broadcast on Sunday, disclosing plans to talk with Mr. Trump about how to subvert the international agreement reached last year with Iran that limits its nuclear capabilities in exchange for sanctions relief. During the campaign, Mr. Trump said that dismantling “the disastrous deal with Iran” was a priority, but he has not specified what he would do. Israel considers Iran a prime security threat.

“I think what options we have are much more than you think,” Mr. Netanyahu said. “There are ways, various ways of undoing it.” He did not explain them.

“The only good thing I can say about the deal with Iran is that it brought the Arab states and Israel closer together,” Mr. Netanyahu said.

The relocation of the embassy would undoubtedly cause an Arab backlash. One reason Israeli leaders have generally not pushed the issue is concern that it could harm their relationships with Jordan and Egypt, even threatening longstanding peace treaties with those neighboring countries.

Asked about Mr. Barkat’s prediction, Palestinian diplomats in the United States were blunt.

“I hope that the new administration will carefully measure its policy toward the city and continue to adhere to the declared and official position of the U.S. about Jerusalem,” Ambassador Maen Rashid Areikat, the chief Palestine Liberation Organization representative to the United States, said in an email. “Taking sides with Israel on such a sensitive and highly emotional issue will further escalate tension in an area that is already volatile.”