Curry was famously sacked as anchor of Today and became a general assignment reporter this summer amid rumours that her co-host Matt Lauer no longer wanted to work with her.
Jolie is thought to have developed a friendship with Curry over the years due to the journalist's dedication to covering the crisis in Darfur.
The Kung Fu Panda 2 actress reportedly contacted NBC in the wake of Curry's demotion to make her displeasure of her friend's treatment known.
An insider told Radar Online: "Angelina has tremendous respect for Ann because of the work she has done on bringing awareness to Darfur.
"Ann has developed a professional relationship with Angelina and Brad, and they trust her implicitly because of her integrity.
"Their working relationship has developed into a friendship, and it meant the world to Ann that Angelina had reached out to her.
"Angelina made it clear to Ann that no-one from the current Today show cast would get an interview with Angelina or Brad, and with rumours of an upcoming wedding for the couple, NBC will lose any interviews with the actors in the future if Ann isn't allowed to do it."
Jolie has not publicly commented on this latest report, nor has Curry.
Curry's professionalism was also recently praised by her former Today co-anchor Katie Couric, who predicted that the journalist will "land on her feet".
Watch Ann Curry's Today farewell below: