SAN JOSE — San Jose’s mayor has tall ambitions.

Seeking to reshape downtown San Jose’s low-slung skyline of boxy office towers, Mayor Sam Liccardo is eyeing ways to raise the maximum heights of buildings in the city’s urban core.

Much of downtown San Jose lies beneath or near the flight paths of airplanes arriving at, or departing from, San Jose International Airport. As a result, the city’s downtown skyline has a flattened and undistinguished look. Depending on the downtown section where a building might be constructed, city rules place height limits on buildings ranging from roughly 120 feet to 200 feet — which works out to roughly 10 to 16 stories.

“Transforming our downtown skyline and maintaining a world-class international airport each constitute important fundamental long-term economic objectives,” Liccardo wrote in a memo to the City Council, issued this week. “We’ve had to manage conflicts between the two.”

The mayor surmised that new technologies might make it possible for higher buildings to coexist with a busier airport.

“In 2006, the City commissioned an Airport Obstruction Study to determine impacts and heights of high-rise development to airline service, but aircraft technology and the airline mix at the airport have changed considerably over the last decade,” Liccardo’s letter said.

Airport proponents seek to maintain caps on building heights downtown to ensure the airport is attractive to an array of airline carriers, especially those providing international flights.

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Downtown boosters, though, urge relaxed building-height limits as a way to help the downtown offer a more dramatic and visually appealing skyline.

This issue could gain urgency amid interest by Google to move as many as 20,000 of its employees into a downtown San Jose area near Diridon Station and the SAP Center sports and entertainment complex.

“Downtown San Jose and the Diridon Station area remain subject to height constraints,” Liccardo stated in his letter this week.

City officials say as many as 6 million to 8 million square feet of offices and other commercial spaces could be built near the Diridon train complex.

“It’s great to have the support of the mayor on this,” Scott Knies, executive director of the San Jose Downtown Association, said of the effort to consider raising limits on building height.

An attempt was made around 2006 to raise the downtown area’s height limits. The city commissioned a study into how proposed buildings might obstruct flights into and out of San Jose airport. Then an economic crash made that study a moot point.

“The Great Recession happened in 2008, so we stopped building high rises in San Jose and the airport shed flights, so it was no longer an issue,” Knies said Tuesday.

Now, with a booming economy, and an ever-busier airport, the two competing areas of interest could clash again.

“It appears long past time to re-evaluate the Obstruction Study, with a goal of determining if changes can be made — consistent with FAA and airline safety requirements — to maximize potential development densities in the downtown,” the mayor stated in his letter.

Federal Aviation Administration officials said the FAA doesn’t specifically set height limits on buildings near airports. But it does have power to undertake reviews.

“Under federal law, the FAA has to be given the opportunity to review any proposed structure over 200 feet high anywhere in the country, and shorter proposed structures if they are near airports,” FAA spokesman Ian Gregor said Tuesday.

The mayor specifically is seeking $100,000 to study the matter.

“If we can go higher with our buildings, it gives you a lot more options about what you can do with the architecture,” Knies said. “You could have some spires and interesting buildings in downtown San Jose. It wouldn’t just be mesas and boxy buildings.”