Chicago aldermen were assured Thursday there is no financial risk — and no additional cost — to borrowing $4 billion to start the ball rolling on an $8.5 billion O’Hare Airport expansion plan, even without support from American Airlines.

Between briefing small groups of aldermen, Deputy Mayor Bob Rivkin scoffed at American’s threat to file a lawsuit, shrink its dual-hub at O’Hare — or do both — in a high-stakes battle over five additional gates awarded to hometown United Airlines and American’s spurned demand for three additional gates.

“They’re looking for a couple more gates but, in the end, they’re going to be a signatory because it’s the only rational thing for them to do,” Rivkin said.

“To use the airport as a non-signatory would be irrational in their position. They would have no control. They would have no input. They would have no assurance of gate space or club space. They couldn’t build out what they want to build out.”

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At an Aviation Committee meeting next week, Emanuel wants aldermen to clear the project for takeoff and authorize $4 billion in borrowing to get it started.

On Thursday, Rivkin said the risk is “very low” that American’s steadfast opposition could force the city to pay a higher interest rate, making that money more expensive to borrow.

“We foresee no problems financing the project — whether or not American is a signatory,” Rivkin said.

“The issue really in the end is, what’s the demand for the airport? Because that’s what generates landing fees and rents,” he said. “And the demand for the airport is so strong that the markets are not concerned about the revenues being generated.”

Determined to slow the plan down, American created a website — keepORDcompetitive.com — to marshal support from the airline’s 9,300 Chicago-based employees, as well as the passengers who fly to, from or through O’Hare.

Those who sign their names will receive a phone call from American to give them “guidance on what to say to your officials, then patch you directly to them.”

“At O’Hare, one regional gate can be used nine times a day. Five extra gates translates into 45 additional flights a day or up to two million passengers a year,” the website states. “The last minute deal between the city and United limits consumer choice, raises airline fares and stifles competition. … Chicagoans and travelers passing through will ultimately end up paying the price.”

American spokesperson Leslie Scott refused to comment on Rivkin’s claim that O’Hare’s second-largest carrier will have no choice but to sign on.

“If we have to, we will weigh what our other options are. But right now, our focus is on getting our message out,” she said.

Not to be outdone, United Chief Operating Officer Greg Hart sent an email to the airline’s Chicago area employees encouraging them to reach out to the mayor’s office and their local alderman.

The mayor’s plan calls for demolishing Terminal 2 and replacing it with a new “global terminal” shared by United and American Airlines that would accept both domestic and international flights.

The massive, multiyear makeover also calls for dozens of new gates and additional concourses.

City Hall believes it can bankroll the $8.5 billion project without another infusion of federal funds from President Donald Trump, with whom Emanuel has been engaged in a battle over issues of crime and Chicago’s status as a “sanctuary city.”

“Airlines are willing to pay the landing fees and rents for their terminal space that aggregate to billions of dollars over time. We’re modernizing the airport, the governance structure and the rates,” Rivkin said Thursday.

Rivkin, who served as a top aide to former U.S. Transportation Secretary Ray LaHood, said it’ll be up to Congress to decide whether to raise the $4.50 “passenger facility charge” tacked on to every airline ticket.

“If we get it, we’ll put it to good use … to improve O’Hare. But that is a national issue that is being considered by Congress,” Rivkin said. “It has nothing to do with this deal and it’s not necessary in order to make this deal happen.”