The board is also expected to discuss plans for Lufthansa to take jets for Eurowings from Air Berlin (AB1.DE), sources have said, to help it become the third largest low-cost airline in Europe after Ryanair and easyJet.
Lufthansa said this year it was discussing how to bring Brussels Airlines, which has 49 planes, into its Eurowings platform, which has about 90 planes now.
Brussels Airlines is strong on routes to Africa, where the Lufthansa network has gaps, and the German carrier has said it will look at ways to keep some of the branding.
Lufthansa bought 45 percent of Brussels Airlines owner SN Airholding in 2009 for 65 million euros ($73 million), with an option to acquire the rest from 2011.
Because Lufthansa has loaned 45 million euros to Brussels Airlines, the German carrier can buy the rest for as little as 2.6 million euros more, which has irked Belgian shareholders of the holding firm, Belgian daily Le Soir has reported.
A person familiar with the matter confirmed the figure of 2.6 million euros.
The concept for bringing Brussels into the Lufthansa Group must now be discussed in detail, a spokesman for the German airline said following the supervisory board's decision.
Lufthansa had delayed a decision about whether to exercise its option to buy all of Brussels Airlines after fatal attacks at the airport and metro system in the Belgian capital in March.
Brussels Airlines served a record 7.5 million passengers in 2015 and made a record net profit of 41.3 million euros. Passengers numbers decreased in March and April as a result of the attacks but have been recovering since.
The transaction, is expected to be concluded at the beginning of 2017 after it has held discussions wih SN Airholding shareholders, Lufthansa said in a statement.