American Airlines Group Inc. is taking a preliminary look at possible sites for a new headquarters as it approaches the one-year anniversary of the merger with US Airways.

The airline may decide to leave Fort Worth, Texas, where its been based since 1979, or opt to do nothing, Chief Executive Officer Doug Parker said after a speech today to the Fort Worth Chamber of Commerce. It’s been rare in the U.S. industry for a carrier to shift base to another city.

“We have a perfectly acceptable facility today, and just wondering if there might not be a better opportunity,” he said. “We’re investigating whether that might be the case.”

Some of the locations American is considering are outside of Fort Worth, he said, without being more specific. There is no timeframe for conducting the search and “it’s not at the top” of American’s list of priorities now, Parker said.

American moved its headquarters to Fort Worth from New York in 1979, and into its current campus near Dallas-Fort Worth International Airport in 1988. The carrier retains some operations at US Airways’ old headquarters building in Tempe, Arizona.

JetBlue Airways Corp. elected to keep its headquarters in the New York City area in 2010 rather than move to Orlando, Florida. United Airlines parent UAL Corp. shifted its headquarters to downtown Chicago from suburban Elk Grove Township, Illinois, in 2006. The site remained the base for United Continental Holdings Inc., created in a combination with Continental Airlines in 2010.

To contact the reporter on this story: Mary Schlangenstein in Dallas at maryc.s@bloomberg.net. To contact the editors responsible for this story: Ed Dufner at edufner@bloomberg.net.

Photo Credit: American is looking into moving its headquarter, or getting breaks from Fort Worth. American Airlines