Sources within the committee said they could be done by tomorrow morning and have the report tabled in the afternoon.
Speaking to The Standard on phone from Mombasa, Majority Leader Kimani Ichungwa was upbeat that they will conclude their work on time.
"We began writing the report today and we expect to complete it in a short time to allow those approved to begin serving in government. We are not sure when we will finish but at least before the end of the week," said Ichungwa.
The law requires the report to be tabled in the House within 14 days after submission of the names to Parliament.
However, another MP in the committee who sought anonymity said they would try and fast-track the report.
"Once tabled in the House, I see the possibility of the members finishing the debate and approving the nominees. So the CSs could be sworn in on Wednesday and attend their Cabinet meeting on Thursday if the President wishes," said the MP.
"Should the report be tabled in Parliament tomorrow, the names will be forwarded to the president for swearing-in," he added.
When the House resumes tomorrow, MPs will have the opportunity to adopt the report, reject it or move amendments.
The legislators broke for a shot recess on October 14, to pave the way for the vetting.
Another committee member who sought anonymity said they were dissatisfied with a particular nominee who performed 'below par' during vetting.
The member said they might not approve all the 22 nominees.
Should the committee or MPs reject any name, the president will be expected to nominate another candidate.
It is expected that the battle between Kenya Kwanza and Azimio will play on the floor of the House.
Azimio camp is expected to raise some issues about some nominees.
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Public Appointments (Parliamentary Approval) Act states: "Where the nomination of a candidate is rejected by Parliament, the appointing authority may submit to the relevant House the name of another candidate, and the procedure for approval specified in this Act shall apply accordingly.''
Most of the Cabinet nominees are politicians and allies of the president, a few are new faces that many Kenyans saw for the first time during vetting.
Integrity concerns popped up, with Azimio MPs saying they will adhere to Chapter Six of the Constitution when the names are tabled in the House.
Some of the nominees were at pains to explain their past as members took them to task over a number of issues they had been linked with.