A business associate of the Hollywood couple – who already have six kids – told the Express that plans are moving forward to bring a girl orphaned by the conflict into their family.
Angelina, 39, and Brad, 51, have three biological children, Shiloh, eight, and six-year-old twins Knox and Vivienne, and three adopted - Maddox,13, from Cambodia, Pax, 11, from Vietnam, and Ethiopian Zahara, 10.
Now they want to save another from the horror of war-torn Syria.
The source told The Express: "She has been moved to tears on several occasions over the plight of youngsters orphaned in the Syrian conflict.
"Now she has sorted out her health issues, she and Brad believe the time is right to adopt another orphan from there, most likely a daughter."
And they want to do it this year, the associate told The Express.
The friend added: "This is something that has become very close to their hearts.
"They would like to accomplish it, if possible, before the end of summer because, even though they are both busy, their diaries are relatively light for most of 2015."
As special envoy for the UN High Commissioner for Refugees, Angelina has made more than six visits to Syrian refugee camps and has seen first-hand the atrocities there.
At least 70,000 children have lost their fathers and another 3,700 more have lost both parents who were either fleeing war, thrown in prison or killed.Angelina implored the world 'to save a generation of traumatised, isolated and suffering Syrian children from catastrophe' during a speech in November 2013.
Last month the Oscar-winning actress revealed that she could not biologically have children again as she had her ovaries removed.
She had the operation to prevent cancer cells from taking over the organs after her mum, Marcheline Bertrand, died from cancer in 2007.
Two years ago, she had a double mastectomy as another preventative measure.
The friend told the Express: "Angelina's feeling good about turning 40 in June with a clean bill of health but what will make her happiness complete is seeing a new little face at the dinner table."