Even if Australia's richest person, Gina Rinehart, has extended the olive branch of peace to her two estranged adult children, chances of the bitter and much publicised family feud coming to end appears weak.

Ms Rinehart, whose son John Hancock and daughter Bianca Rinehart have petitioned that she be removed as trustee of a fund created by their maternal grandfather and estimated to contain $4 billion, offered to have a co-trustee appointed to appease the two.

But John was quoted by The Australian as saying he could not see his mum staying as a trustee because of the seriousness of their allegation. However, John added he is not yet in a position to evaluate the offer sent by Ms Rinehart in a letter.

"A trustee could hardly remain in any capacity in view of the claims of past serious misconduct that may require further action," he said.

John wanted himself and Bruce Carter, a businessman from South Australia, to be nominated as the trustees.

Judge Patricia Bergin, who presides over the case, said the open letter by Ms Rinehart was a big step in settling the differences among members of Australia's wealthiest family.

The feud has been a fodder for media, prompting Ms Rinehart to subpoena two journalists to reveal their sources which served as basis of their articles on the court case.

On Tuesday, Justice Janine Pritchard rejected her subpoena for The West Australian journalist Steve Pennells to reveal his source, which Ms Rinehart said she needed for a private arbitration hearing in New South Wales.

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