The feds are investigating Gov. Cuomo’s administration for hiring people to work in the governor’s office but paying them through state agencies and public authorities, the Albany Times Union reported Friday.

Hiring well-compensated political appointees to work for the governor’s office but paying them from other state entities let Cuomo and his predecessors beef up their staffs without getting slammed for hiking their budgets.

FBI agents have grilled people in the governor’s office who are paid by agencies or authorities, about how they were hired, the paper reported, citing sources.

In some cases, hiring letters said employees would be working for the agency or authority even though they were actually going to work for the governor.

The feds are also looking at whether workers in the Executive Chamber had any job duties connected to the agencies or authorities that paid their salaries.

An FBI spokeswoman did not confirm or deny the probe and it’s unclear what law or laws might have been broken. At least some state agencies receive federal funding, which could explain the Justice Department’s interest.

A GOP source was skeptical.

“What crime? It’s legal and it’s been going on for years. Only angle for a criminal case is if they are being paid federal money or part of a federal grant and they are not working on the project the money is designed for,” the source said.

A Times Union report a year ago revealed that more than 40 percent — 89 out of 209 — of the Executive Chamber staff was on the payroll of public authorities or agencies.

That number grew in March when the governor announced 27 new hires or promotions — with all but five being paid by an agency or authority.

Many of the new political appointees were veterans of the Obama administration or of Hillary Clinton’s presidential campaign who were out of a job.

The hires fueled speculation that Cuomo was eyeing a 2020 presidential run.

Team Cuomo called the Times Union’s report “absurd” and said the practice has been going on for decades.

“‎The agencies are all part of the same executive branch, and this administration follows the exact same lawful hiring process we inherited from previous administrations stretching back decades. If there are questions about it, call George Pataki,” said Cuomo spokesman Richard Azzopardi.

“In this environment, anyone can ask about anything, but the fact is the longstanding practice of detailing staff from agencies to work in the Executive Chamber dates back over 50 years to at least the Rockefeller administration and extends to the White House and the federal Department of Justice,” he said.

“Given that the Federal Department of Justice and the White House have a long history of utilizing this practice, perhaps the FBI can investigate them when this is charade is over.”

The paper reported that some employees do have some connection to the agencies or authorities they are paid by while in others they do not.

In one case, ex-New York Post journalist Tom Topousis was hired in 2015 at a $125,000 salary as a “special assistant” at the Office of Children and Family Services, a child protective services agency — though his real job was speechwriter for the governor.

Another speechwriter, Jamie Malanowski’s, earns $120,000 from the Affordable Housing Corp., a quasi-governmental agency that helps subsidize affordable housing projects, but also writes speeches for Cuomo.

One of the March hires was Joel Wertheimer, who coordinated briefing materials sent to President Obama.

In his new job as a staff secretary for Cuomo, Wertheimer, who left the administration in September, was paid $120,000 salary by the Office of Alcoholism and Substance Abuse Services.