In the coming weeks, Gov. Andrew Cuomo is expected to announce details of a $10 billion face-lift for one of America’s busiest airports.

The plan is expected to provide upgrades to John F. Kennedy International Airport, in Queens, including new roads for motorists, improved taxiways for aircraft and a modern, more consolidated terminal layout.

But it won’t include one element that planners say is essential to handling rising demand in the coming decades: a new runway.

“Right now, a new runway is not on the table,” said Rick Cotton, the executive director of the Port Authority of New York and New Jersey, which runs JFK.

The airport served a record 59 million passengers last year, up 23% from 48 million passengers in 2008, according to Port Authority data. JFK’s four runways are sufficient to handle projected passenger growth through 2035, Mr. Cotton said. By then, the airport expects to serve 80 million passengers, he added.

The Port Authority needs to consider a new runway now, people familiar with the airport’s development say. In fact, the agency had considered a new runway as far back as 2011, according to the people familiar with the matter. But the agency has avoided publicly raising its desire for a new tarmac, in part because the issue is so politically charged.

“Everyone wants a new terminal,” said one of the people familiar with the planning. “Not everyone wants a new runway.”

Mr. Cuomo’s office referred all questions to the Port Authority. Mr. Cotton, in a statement, said that the modernization plans about to be unveiled for JFK are needed to meet projected passenger growth through the 2030s. “We need to transform JFK into an airport that can actually meet 21st century demands before we start considering new runways,” he said.

Airport runway projects typically are controversial because of noise and pollution concerns. The Port Authority has an added difficulty at JFK because a new runway likely would be built over Jamaica Bay, an 18,000-acre wetland estuary. It also could cost billions of dollars.

The Port Authority is a bistate agency controlled by the governors of New York and New Jersey. Mr. Cotton was appointed to lead the agency last year by Mr. Cuomo.

The agency runs the region’s three major airports: JFK, LaGuardia Airport and Newark-Liberty International. Together they act as a regional air system, with JFK and Newark in New Jersey serving a mix of domestic and international passengers, while LaGuardia, in Queens, focuses on domestic passengers.

The Port Authority was a principal sponsor of a 2011 study by the Regional Plan Association, an urban-planning organization. The study predicted that total demand at the three airports would grow to 150 million passengers by 2030, up from 104 million passengers in 2010.

Since then, demand has increased more rapidly. Last year, the airports handled a record 132 million passengers combined, according to the Port Authority.

In a report published earlier this year, the Regional Plan Association said JFK needs two new runways, but it noted that so far the Port Authority hasn’t indicated any plans to expand capacity.

Agency officials say more time is needed to study the effects of a new air-traffic control system, which is being rolled out nationwide in the coming years. But the Regional Plan Association report noted that previous findings by its staff and by the Port Authority concluded that even with a new air-traffic system, additional runways would be needed to meet demand.

Chris Ward, who stepped down as Port Authority executive director in 2011, said that at the time, officials believed it would take between 20 and 25 years to plan and build a new runway.

“There’s no denying that this is a question of math,” Mr. Ward said recently in an interview. “If you know the forecast is for this amount of travelers and they want to come to New York, how do you solve the equation?”

Write to Paul Berger at Paul.Berger@wsj.com