In the weeks since Hillary Clinton's shock election defeat to U.S. president-elect Donald Trump, a rumour has taken hold among New York City's political chattering class: could she challenge Mayor Bill de Blasio's re-election bid this year?

Discussion of a possible Clinton campaign intensified last week when conservative news website Newsmax reported that Democrats unhappy with de Blasio were pressing her to run. Stories soon appeared in various outlets, including the New York Times and the New York Daily News.

Still, the chances seem remote. Although the mayor of the largest U.S. city is often seen as a national figure, it could be seen as a step down for Clinton, 69, a former U.S. secretary of state who came tantalizingly close to winning the White House two months ago.

'There is zero chance that's going to happen'

"I'm a Brooklyn kid, and my comment is, fuhgeddaboudit," said Douglas Muzzio, a political scientist at Baruch College in New York and an expert in city politics. "There is zero chance that's going to happen."

Clinton has yet to say what she plans to do next, and representatives of Clinton's presidential campaign did not immediately respond to a request for comment on Sunday.

A street sign on the corner of President Street and Clinton Street in Brooklyn is seen Nov. 8. In the presidential election, Clinton won more than 80 per cent of the votes in heavily Democratic New York City. (Saul Martinez/Reuters)

A Clinton confidante, Neera Tanden, said on CNN on Sunday that Clinton was focused on helping children and families in her next role.

"I don't expect her to ever run for any elective office again," Tanden said when asked if Clinton would run for mayor.

Clinton has history, support in New York

De Blasio, a fellow Democrat who won his first term in 2013, has had some rocky moments, including state and federal corruption investigations that have reportedly examined his fundraising tactics.

A high-profile figure in the party's liberal wing, De Blasio supported Clinton in the presidential primary after some public waffling. A spokesman for his re-election campaign declined to comment on a potential Clinton candidacy.

De Blasio speaks in support of Clinton to the overflow crowd outside the former nominee's election night rally in New York on Nov. 8, 2016. A spokesman for his re-election campaign declined to comment on a potential Clinton candidacy. (Mark Kauzlarich/Reuters)

In the presidential election, Clinton won more than 80 per cent of the votes in heavily Democratic New York City, despite Trump's status as a native son born in the borough of Queens.

Clinton first moved to New York State in 1999 in order to run for the U.S. Senate, winning election the following year. She lives with her husband, former president Bill Clinton, in Chappaqua, N.Y., about 48 kilometres north of the city.

Under state law, Clinton could run for mayor as long as she became a city resident by the election, according to the Times.