Wealthy, high-performing schools that once looked as if they might lose money under the mayor’s new funding plan can instead expect a windfall of extra cash if they agree to accept students from failing schools, Department of Education officials confirmed yesterday.

High-performing schools would receive $2,000 for each student transferring from a school found failing under the No Child Left Behind Act, an effort by the department to solve a old problem with a cornerstone of the federal law.

Good schools take part in deciding how many seats they offer to transfer students — often not a desirable group because they can potentially pull down test scores.

“There’s a well-known supply and demand issue,” a department spokesman, Andrew Jacob, said.

Last year, less than a tenth of 185,000 city students eligible under federal law applied to transfer, and little more than half of those were offered a seat in a new school. Only a fraction of those eligible — 3,494 — actually transferred.

The extra funding attached to transfer students would almost double the amount per pupil that some schools receive in tax levy dollars, which pay for operating costs such as teacher salaries — a financial incentive department officials hope will encourage schools to offer more seats.

On Monday, the department is expected to release the complete list of new “weights” attached to needy students — including English language learners, low-income students, and low-performing students — under the plan, known as weighted student funding.

The department released the transfer student weight early so that school principals could offer more seats for the transfers before their budget deadline.