The couple has been estranged ever since she cut him out of her life for insinuating she was unbalanced in a tearful 2002 TV interview.
In a recent interview, Jolie defended her actions, stating, "He said some very ugly things to me about what he thought I was like as a person and how I was conducting my life... I don't have to listen to what he says. I don't have to care. And I don't have to have him in my life."
But it seems the mother of four, who lost her own mother to cancer in January, is now softening towards her father.
She recently told London's Evening Standard newspaper, "I am hoping my relationship with my father will be more private in the future.
"At the end of the day we both wish the best for each other and we'll try to start communicating in some way."
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