The company issued the request for proposals on Friday and requires that submissions be in by mid-December, spokesman Doug Adler said in an email. A decision on the site selection is expected early next year.
Adler declined to name the locations under consideration.
But people familiar with the discussions said that South Carolina, Alabama, Texas, Utah, California, Kansas, Missouri and Washington state are among the possibilities.
The airplane maker is negotiating for a site to build the aircraft after the International Association of Machinists and Aerospace Workers union earlier this month rejected a contract offer that would have meant the work stayed in the company's traditional manufacturing site in the Puget Sound area, but with diminished benefits.
Unions representing more than 60,000 Boeing workers, most of whom work in Puget Sound, issued a joint statement late Friday saying they are ready to meet the challenge of designing and manufacturing the 777.
Adler said Boeing is looking for one or more locations for work that will include wing fabrication and final assembly.
"We still have no plans to re-engage with the machinists in Puget Sound," he said on Saturday.
The contract extension for Boeing workers in the Puget Sound area would have cut pensions and health-care benefits, slowed the rate of wage increases for new employees and provided a $10,000 (6,161.81 pounds) cash bonus per member.
Boeing launched a long-awaited new version of its 777 passenger jet with 259 orders from four airlines at the Dubai Airshow in mid-November.
Boeing Chairman James McNerney said the order, based on commitments worth some $100 billion at list prices, was the largest combined order in the company's history.
(Susan Kelly and Alwyn Scott - Reuters)