The Federal Aviation Administration is close to approving Boeing’s approach to fixing the batteries on its 787 jets, and tests could begin next week, federal and industry officials said Wednesday.

The FAA could still demand changes in Boeing’s proposed new battery design if problems develop in the laboratory and in flight tests, which will take several weeks. But the decision to start the tests will mark a major step in Boeing’s efforts to get the innovative jets, which have been grounded since mid-January, back in the air.

The federal approvals are expected to come late this week or early next week, even though some battery experts remain concerned that investigators have not found the precise cause of two incidents in which the jetliner’s new lithium-ion batteries emitted smoke or fire.

The National Transportation Safety Board has found that a short-circuit in one cell caused a battery in a jet parked at a Boston airport to overheat and burst into flames on Jan. 7. The board plans to release a preliminary report on that incident today.

The FAA’s Seattle office on Wednesday was wrapping up its recommendation to approve Boeing’s plan to carry out the tests needed to certify that the battery fixes would work, federal officials said.