New York City Schools Chancellor Carmen Fariña warned Tuesday that the city is considering expensive contingency plans if the State Legislature and Gov. Andrew M. Cuomo fail to extend mayoral control of public schools.

With two days left in the legislative session, Fariña told reporters in Albany that the move back to the old system — a board of education that does not answer to a single person — would cost millions of dollars, although she didn’t provide a specific amount.

“If we are going to do what’s best for the children, someone has to be accountable,” said Fariña, who was appointed in 2014 by Mayor Bill de Blasio, a Democrat. “Right now, the mayor is accountable and I’m accountable to the mayor.”

Albany must greenlight any extension of mayoral control by Wednesday night’s scheduled end of the legislative session or the system reverts to before then-mayor Michael Bloomberg secured control in 2002. Prior to that, some 32 independent districts made decentralized decisions, and the board of education picked a chancellor. That system was long panned as inefficient and unaccountable.

The Democratic-controlled Assembly is pushing a multiyear extension. Leaders of the Republican-controlled Senate said they would approve such an extension, but only in exchange for compromises on charter schools, which de Blasio and the Assembly Speaker Carl Heastie (D-Bronx), oppose.

Fariña spoke in the state capital as de Blasio convened a conference call with one of former president Barack Obama’s education secretaries, Arne Duncan, who said, “there’s got to be some compromise.”

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“If we were to lose mayoral control in New York for whatever reason, I think it’s unquestionable that harm would be done to children,” said Duncan, but he acknowledged he wasn’t familiar with the specifics of what State Senate leader John Flanagan (R-East Northport) wants.

“I honestly don’t know the details,” said Duncan, a longtime supporter of charter schools, which are publicly funded but independent educational institutions largely free of the rules governing traditional district schools.

Asked whether he would be willing to compromise, de Blasio said it is the leaders in Albany who must negotiate.

“Lock yourselves in the room until you get there,” de Blasio said of state legislators.

Fariña said she’s worried about the schools if the old system is put in place.

“I can’t tell the board what to do,” she said, noting to reporters that test scores have risen citywide under de Blasio.

Heastie reported no substantive movement on the issue in recent days. He said he wasn’t certain he, state Senate leaders and Cuomo will be able to agree to even a one-year extension by Wednesday night.

“Two days in Albany is a lifetime,” Heastie said this week. “The school system has improved in the four years that Mayor de Blasio has been mayor.”

Flanagan spokesman Scott Reif said his boss favors mayoral control and charter schools.

“We’re talking about issues wholly related to education,” he said. “It’s all about the New York City school system.”