"It'll happen this week," Ainge told Chris Forsberg of ESPN Boston.
Green averaged 9.8 points and 3.3 rebounds in 26 games in Boston. Green was acquired at the trade deadline in the deal that sent Kendrick Perkins and Nate Robinson to the Oklahoma City Thunder in exchange for Green and Krstic. In 75 total games this season, Green averaged 13.3 points and 4.8 rebounds.
The qualifying offer is worth $5.9 million over one year. Boston will be able to match any offer given to Green, who is a restricted free agent, on the open market. If he does not receive any additional offers, Green can sign the deal and will become an unrestricted free agent next offseason. In addition, the Celtics can work out a long-term deal with him.