A veteran FDNY paramedic was busted a year ago on felony charges of distributing child pornography, but has stayed on the city payroll while negotiating a plea in hopes of saving his job, The Post has learned.

Aaron C. Aguirre was indicted last March 14 after admitting that he communicated by e-mail with an undercover agent posing as the father of a 5-year-old girl, records show.

A complaint alleges that Aguirre, 34, “expressed his sexual interest in the agent’s daughter, as well as other young children,” Brooklyn federal judge William Kuntz II said in court last week.

The complaint also alleged that Aguirre ultimately sent the agent files containing “images of toddlers’ private parts and pornographic videos of children between the ages of 4 or 5 and 7 or 8,” the judge said.

Aguirre’s lawyer, Oliver Storch, told the court his client was negotiating “a new plea agreement” with the US Attorney’s Office. Distributing child-porn normally carries penalties of five to 20 years in prison.

“Mr. Aguirre is not a public officer as firefighters and police officers are, so upon conviction of a felony, he would not automatically lose his employment with the city of New York,” Storch said.

Storch told The Post, “He’s in the business of saving lives, and he’s obviously devastated and saddened by these charges.” The lawyer declined to comment further.

A fellow paramedic called it “absurd” to put someone accused of having sexual interest in children on a job that involves touching patients.

FDNY spokesman Frank Gribbon said, “We would seek termination of any employee convicted of a felony.”

Aguirre, who joined the FDNY in 2008, has served as a Haz-Tac and rescue paramedic instructor. He took home $95,953 last fiscal year, including $32,645 in overtime, according to SeeThroughNY.

After his arrest, Aguirre was suspended a maximum 30 days, then placed on “restricted duty,” meaning “no patient care, no contact with the public, no access to computers” and no OT, Gribbon said, adding that Aguirre is “under direct supervision.”

The FDNY did not inform the state Health Department, which licenses paramedics, about Aguirre’s arrest until after The Post inquired last week, officials said.

The agency is required by law to “report all arrests and suspected crimes to the Department of Health. Failure to comply with regulations will result in an investigation and possible enforcement actions,” said state Health Department spokeswoman Jill Montag.

The state will pursue “an immediate suspension” of Aguirre’s certification, Montag said.

“Any incident that violates public health law, especially a crime involving children, will be immediately investigated and the department will aggressively pursue the strongest penalty possible under the law.”