This followed a complaint relating to her reports that have been criticised as shoddy by opposition parties and civil society.
Chairman of the portfolio committee on justice and correctional services Mathole Motshekga confirmed on Saturday that the committee would discuss the matter next month.
He said since it had been referred by Mbete, it would be up to the committee to decide to hold an inquiry or not.
“The committee will consider the matter,” Motshekga said.
“We will consider the referral because the matter has been referred to us by the Speaker.
“Our committee is competent enough to deal with it.”
The DA had complained that Mkhwebane was not fit to hold office after she produced shoddy reports on the Estina dairy farm project and for not properly handling the Ciex report into the bailout of Bankorp.
She was questioned recently for exonerating former Free State premier Ace Magashule and former mineral resources minister Mosebenzi Zwane on their role in the Estina project and awarding it to the Guptas.
The DA and Council for the Advancement of the South African Constitution have taken the report on review to the High Court in Pretoria.
Mkhwebane is sitting on a mounting legal bill because her reports have been challenged in court.
The official opposition wants her to be removed from her position.
Motshekga said it would not be dictated by anyone on how to do its work.
The committee will meet next month to decide whether to hold an inquiry or not.
DA chief whip John Steen- huisen has said he wants to make a presentation to the committee on why Mkhwebane should be removed.
But Motshekga said: “We don’t need an extra hand from anybody.
“Steenhuisen, if his party wants him to participate in the committee, he can participate.
“Any member sent by their party can participate in the committee, but there is no special dispensation for Steenhuisen to make a presentation,” said Motshekga.
“We are quite well informed about the issues, we will be able to make a decision there.
“We are not holding an inquiry on that day (of the meeting).
“We will decide whether an inquiry is needed or not.
“If we decide to hold an inquiry that will be subject to a process and that process is subjected to the programme of Parliament,” he said.