The Post and Courier of Charleston reported that authority attorney Arnold Goodstein told the authority board on Tuesday that the FAA is "asking a lot of questions" about the sale of the 320 acres of land.
Authority Chairman Andy Savage said the federal agency has concerns about the $12.5 million price for the land and is concerned the deal could affect the airport's overall operations.
The FAA must approve the sale. Boeing South Carolina spokeswoman Candy Eslinger would not talk about the case.
Goodstein, airport officials and Boeing representatives met with FAA representatives in Washington this week to move the deal along. Savage said aviation authority officials made it clear that while it didn't get the deal it wanted on the land purchase, the authority stands behind Boeing.
The aviation authority voted in March to sell the land, splitting the difference between a set of appraisals conducted by both parties.
The FAA is looking at the authority's initial appraisal of $27.6 million, Savage said. But that figure appraised the land as if it were ready for development and didn't include the costs of filling numerous wetlands and removing a radar site.
Boeing has not said specifically what it plans for the site.
The company announced in April that it will add at least 2,000 jobs during the next seven years. It already employs 6,000 workers who assemble the 787 Dreamliner jet.