The city will allow seven schools to change their admissions policies to make sure they enroll a diverse mix of students, sources said Thursday, more than a year after a group of principals began lobbying to do so.

The education department would not immediately confirm that the plans had been approved. But people with direct knowledge of the schools’ proposals, who were not authorized to speak publicly, said an official announcement was expected Friday.

The schools will be able to reserve a portion of their available seats — anywhere from 10 to 60 percent — for low-income students, English learners, students who are involved in the child-welfare system, or children who have incarcerated parents, according to sources.

The expected announcement would represent a significant shift for Mayor Bill de Blasio, who has spoken about the value of school diversity but has been reluctant to make policy changes to promote it. The previous administration let one district school, P.S. 133 in Park Slope, adopt a diversity-focused admissions policy, but the current administration has so far declined to sign off on similar policies that other schools have requested.

The policy shift comes as the city has faced increasing pressure to directly address school segregation and the lack of student diversity at many schools, a push partly sparked by racially charged debates over rezoning proposals in Brooklyn and Manhattan’s Upper West Side. Last month, education department officials bowed to that pressure by moving to strike a footnote from the city’s school admissions code that had been criticized for potentially blocking efforts to create diverse schools.

“Empowering elementary schools to use admissions processes that strengthen diversity is a strong step in our ongoing effort to confront the segregation of our schools,” City Councilman Brad Lander said in a statement. He and Councilman Ritchie Torres co-sponsored a bill, which de Blasio signed into law this spring, that will force the education department to report annually on school demographics and its efforts to increase diversity within schools.

Two schools in Lander’s district — Brooklyn New School and Brooklyn Children’s School — are among those that will be allowed to adopt new admissions policies. The other schools are: the Academy of Arts & Letters in Fort Greene, Brooklyn Arts and Science Elementary School in Crown Heights, the Earth School and the Neighborhood School in the East Village, and Castle Bridge School in Washington Heights, according to people with knowledge of the plans.

In Oct. 2014, a group of principals met with top department officials and floated diverse-enrollment plans similar to that at P.S. 133, which the Bloomberg administration allowed to reserve more than a third of its seats for low-income students and those still learning English. The idea is to preserve a diverse mix of students at the schools even as more white and affluent students enroll. At the start of this school year, several of the principals said they had yet to hear back from the city about their proposals.

But in recent days, advocates who have been pushing de Blasio to do more to promote school integration said they have heard that the city was preparing to allow some of the schools to save a portion of seats — or create “set-asides” — for particular student groups.

“My understanding is that now they’re granting set-asides to certain individual schools,” said David Goldsmith, president of the Community Education Council in Brooklyn’s District 13, where P.S. 133 is located.

Principals from P.S. 133 and three other District 13 schools attended last year’s diversity meeting with top officials, including Schools Chancellor Carmen Fariña. One of the schools was the Academy of Arts & Letters, which has seen its share of low-income students fall from about three-quarters to less than 40 percent over the past several years as the school’s neighborhood has rapidly gentrified. Under its newly approved plan, the school will be able to reserve 40 percent of available seats for low-income students — effectively keeping its share of those students from shrinking any further.

Admissions systems like those the city is set to approve can help schools in gentrifying areas avoid “tipping,” or switching from a mix of students from different backgrounds to a majority of students from middle-class families that are settling in the school’s neighborhood.

While advocates have welcomed the prospect of the city granting individual schools permission to tweak their admissions policies to ensure diversity, they have also argued that district-wide policies are crucial. Otherwise, a school with set-asides might enroll a mix of students while surrounding schools could become increasingly segregated.

“If you solve a problem in one school and create a greater problem in five schools as a result,” said Goldsmith, the CEC president, “what are you really accomplishing?”

Education department spokeswoman Devora Kaye said that the city is working with educators, parents, and lawmakers to promote school diversity.

“Students learn from the diverse experiences and cultures of their fellow students, and it’s important that our schools reflect the diversity of our City,” she said in a statement.