The regulator plans to publish its order in Monday's Federal Register, The Wall Street Journal reported Sunday.
The Journal report said that both Chicago-based Boeing and the FAA had no comment on the matter.
At issue are horizontal flight-control surfaces called elevators located in the tails of the widebody jets, the report said.
The new directive calls for increased inspections of the elevators, and the modification and replacement of parts that control them, the report added.
The elevators assist in raising and lowering the noses of planes while in flight. Problems in the elevator system can change a plane's pitch and cause a possible loss of control, the FAA order said, according the Journal report.
Concerns about the 767 elevator system are not new. In 2000, the FAA issued an order for inspections of 767s to see whether "shear rivets" in the elevator mechanism had broken.
Since then, the FAA has ordered and Boeing has recommended additional tests related the elevator system, the report said.
The FAA directive scheduled to be announced Monday will take effect in March and will require U.S. airlines to replace suspect parts within six years, the report also said.
Foreign regulators are expected to issue similar orders, the report said.
The inspection and repair work are projected to cost airlines millions of dollar, but the FAA said Boeing would pick up the cost of some the work, the Journal reported.
Shares of Boeing closed Friday down $4.66, or 3.3%, at $136.65.