The initial flight tests will gather data on the operation of the troubled lithium ion battery system, the cause of the worldwide fleet grounding that's now into its third week.
Boeing also wants to test a potential fix, the sources said.
But 787 passenger flights won't resume soon. In airline service, the Dreamliner is still likely to stay grounded for weeks, if not months, two sources said.
Even when Boeing arrives at a workable fix, its engineers will have to design, build and thoroughly test the solution.
The FAA ordered the grounding after two serious 787 battery incidents just over a week apart.
First, a battery fire broke out on a parked 787 in Boston early last month. Days later, a smoldering battery forced a jet in flight to make an emergency landing in Japan.
One fix Boeing is looking at closely is a way to strengthen the lithium ion battery's ability to contain any internal overheating and to improve the venting system whereby hot liquid or gaseous products exit the battery box and are directed outside the airplane, two sources said.
But the initial flights will simply gather data on how the battery is affected by changes in temperature during the flight cycle as well as the impact of vibrations during landing and take-off.
According to an industry source, one theory Boeing is investigating is that moisture getting inside the battery may have contributed to the recent incidents.
The National Transportation Safety Board, which is investigating the Boston fire, has so far given no indication that it has determined the root cause.
The resumption of flying, even if only for test flights, would be the first glimmer of hope that Boeing is on its way to resolving the plane's technical problems.