The Australia Post board has agreed to participate in mediation with former chief executive Christine Holgate.
But the board will require Ms Holgate to make public her demands to settle the dispute and the outcome of the mediation.
"Australia Post's lawyers have again written to Ms Holgate's lawyers confirming that Australia Post will participate in a mediation," the board said in a statement on Wednesday.
"Further, given the public interest in this matter and Australia Post's wish to be transparent about it, we have asked that Ms Holgate agree that following the mediation the parties will make public what she asked Australia Post to give her to settle the dispute and also the outcome of the mediation."
Ms Holgate claims she was bullied and unlawfully stood aside for rewarding four senior executives with luxury Cartier watches.
Earlier this week, she threatened to sue the Morrison government over her ousting from Australia Post, naming a deadline of Wednesday evening for senior ministers to agree to mediation.
Ms Holgate demanded Communications Minister Paul Fletcher and Finance Minister Simon Birmingham agree to talks "in order to avoid time-consuming and costly litigation for all parties".
Her statement delivered by lawyer Rebekah Giles warned she would have no option but to consider legal action if the ministers and the government-owned company refused to meet her deadline of 5pm on Wednesday.
"We have been advised the government requires more time to consider the offer to mediate and that Australia Post will not be able to meet the deadline," Ms Giles said.
"Given there appears to be an absence of agreement to mediate this matter expeditiously, Ms Holgate will now have no option but to consider her legal options after the Senate Communications and Environment Committee's report into these matters is released on May 17.
"This was not her preferred method of dealing with this issue, but the ball is in the court of Australia Post and the government to resolve this matter."
The coalition has consistently argued the acrimonious departure is not a matter for the government, but instead one to be resolved between Ms Holgate and Australia Post.
Australian Associated Press