Runaway overtime at the Chicago Police Department isn’t the only item in Mayor Lori Lightfoot’s cost-cutting crosshairs.

She also hopes to hammer out a new firefighters’ contract that eliminates treasured union perks and outdated staffing requirements that cost taxpayers tens of millions of dollars.

“She doesn’t want to have a confrontation, but she’s a tough cookie, and there are some things in the firefighters’ contract that don’t make a lot of sense and should be changed,” a mayoral confidant said Tuesday on condition of anonymity.

“Fires are way down. Emergency medical calls are way up. Yet, this is still a fire suppression department firmly planted in the 1950s and ’60s. Changing that kind of encrusted tradition is extremely hard. But she’s taking a hard look and trying to come up with a plan.”

Sources said Lightfoot delivered her cost-cutting message in a recent face-to-face meeting with Jim Tracy, president of Chicago Firefighters Union Local 2.

The mayor asked for help and cooperation from a union that gave her a pivotal endorsement during the runoff campaign against Toni Preckwinkle.

Sources said the answer was no, setting the stage for contentious negotiations.

Tracy could not be reached for comment.

“They came to appreciate that we’re simply not gonna do business as usual,” the mayoral confidante said.

Another City Hall source noted former Mayor Rahm Emanuel had been close to a new firefighters’ contract that would have traded health insurance concessions for a reduction in daily “variances” from the minimum manning requirement that triggered the bitter 1980 firefighters strike.

That rule requires every piece of fire apparatus to be staffed by at least five employees.

But time ran out before the deal got done.

“If the union was smart, they would have grabbed that deal. But they got greedy. They wanted 15% over five years,” the source said.

For years, Inspector General Joe Ferguson has urged the city to revisit the minimum staffing requirement and eliminate a host of contract sweeteners.

On Tuesday, Ferguson urged Lightfoot to be bold where Emanuel was timid.

“The purpose of OIG’s prior work on this subject was to bring to full light and understanding aspects of the current contract that presented opportunities for savings and efficiencies worth consideration ... in the next bargaining round,” Ferguson was quoted as saying in an statement emailed to the Sun-Times.

The city’s deficit “makes those considerations and opportunities more relevant than ever.”

Emanuel took office in 2011 talking even tougher than Lightfoot is now.

He vowed to take a hard line with firefighters — though his own fire commissioner opposed closing fire houses or reducing the minimum staffing requirement.

Four months later, then-Fire Commissioner Robert Hoff abruptly resigned, leaving firefighters without a champion.

It wasn’t long before Emanuel dropped the other shoe.

He infuriated Local 2 by taking aim at such treasured union perks as holiday and duty availability pay; clothing allowances; pay grades; premium pay; the physical fitness incentive and the 7% premium paid to cross-trained firefighter paramedics.

Emanuel’s plan did not include closing fire stations. But it would have allowed all fire houses with both engines and trucks to be staffed by nine firefighters instead of 10.

Rookie probation would have doubled to 18 months.

In a letter to the rank and file, then-union president Tom Ryan declared Emanuel’s plan “horrendous, insulting and ridiculous.” Ryan dug in for what he feared would be a “long and bitter battle.”

It never happened. Emanuel backed off and settled for a “vanilla” agreement with no cost-cutting concessions.

Never mind that Ferguson had estimated annual savings of $57 million if the number of employees on each piece of fire apparatus was cut from five to four, and that another $14.3 million could be saved yearly by eliminating “duty availability pay” — compensation for being on 24-hour call.

Ald. Gilbert Villegas (36th), the mayor’s City Council floor leader, argued Tuesday that every option now must be on the table, including closing firehouses, to chip away at the city’s $838 million shortfall.

“We are in a financial crisis. There’s gonna have to be concessions made on everything,” Villegas said.

“If the need for firefighters vs. EMTs has changed, we need to change the formula. There are no sacred cows anymore. They’ve all gone out to pasture.”

Mayoral press secretary Anel Ruiz said it is “never appropriate to negotiate a union contract through the media.” But, she stressed that Lightfoot respects “the fearless men and women of the Fire Department along with” their union leaders.

“Together, we will reach an agreement that is fair to the men and women of the department as well as taxpayers, and one that positions the department for success in meeting the fire suppression and emergency response needs of today and the future,” Ruiz said by email.