The 52-year-old actor is also willing to take a polygraph test to prove that he did not cheat with co-star Marion Cotillard, according to the Sunday Mirror. Cotillard and Pitt filmed war film Allied together.
Pitt's bid will come after the shocking split between himself and Jolie which was announced last week.
Pitt and Jolie were allegedly having an argument on the plane when Maddox, 15, their eldest adopted child, reportedly stood up for his mother. Pitt reportedly "lunged" at him at this point.
The incident involving Maddox and Pitt was caught on tape, in which Pitt is reported to be seen "looking drunk" and "yelling".
Pitt has not seen his children since the altercation on the plane.
"Angie hated all the female attention Brad would get," a source told the Daily Star. "She is very jealous and insecure, despite being one of the most beautiful women in the world.
"They had a number of arguments about his closeness to Marion.
"Brad did all he could to reassure her there was nothing going on and even offered to take a polygraph test to prove he was telling the truth.
"Sadly for him, she [Angelina] refused."
Voight told TMZ: "I'm sure she [Jolie] is doing fine. Listen, I'm concerned about anyone who's going through tough times… for the family and for the kids."
Jolie filed for divorce, ending a 12-year relationship with Pitt. The pair married in 2014 after a long-term relationship and they have six children: Shiloh, 10, Zahara, 11, Maddox, 15, Vivienne, 8, Knox, 8, and Pax who is 12. Jolie is currently asking for full custody of the children. However, Pitt wants joint custody.
"Brad has made an effort to make contact and is keen to try and improve the situation between them," a source told the Daily Mirror.
"He's hoping his good relationship with Angelina's family will help to build bridges. He's spoken to her dad Jon and hopes he may be able to play peacemaker.
"It's a very tricky time for the family but Brad hasn't given up hope yet."