Mr MacAskill has fought off calls for him to be sacked over the past two weeks, after he was forced to delay a flagship Bill to remove the centuries-old corroboration rule in criminal trials.
However, his plan for the single force to save £1.1bn by 2026 is being disputed by four MSPs on a powerful Holyrood committee.
The Public Audit Committee carried out a six-month inquiry into the force, but Labour MSPs Hugh Henry and Ken Macintosh, LibDem Tavish Scott and Tory Mary Scanlon were angered after the final, revised, report underwent "substantial changes", removing much of the criticism of the Government, whose majority of MSPs voted it through.
They have now made the unusual decision not to endorse the report after four stormy meetings, and are understood to have produced their own report criticising the complex arrangements to govern and oversee Police Scotland.
The "rebel" report and the official report will now both be issued on Tuesday next week, bringing renewed scrutiny of Mr MacAskill's claims.
One source close to the committee said it was felt the Justice Secretary's £1.1bn figure had "been calculated on the back of a fag packet".
The spat threatens to put more strain on Mr MacAskill who has faced calls for him to be replaced after he put on hold plans to end the requirement for corroboration in the Criminal Justice Bill.
Mr MacAskill has faced a number of controversies, including a boycott of sheriff courts by lawyers over his Scottish Civil Justice Council and Criminal Legal Assistance Bill, which aimed to make some accused pay defence costs and which was only passed with amendments.
He faced anger from US relatives of the victims of the Lockerbie bombing following his decision to release the terminally ill Libyan convicted of the atrocity, Abdelbasset al-Megrahi, on compassionate grounds in August 2009.
The achievability of the £1.1bn saving has been questioned by public spending watchdog Audit Scotland.
Six months into the new police structure, it said Police Scotland and its oversight body, the Scottish Police Authority (SPA), had failed to finalise a strategy showing how long-term savings would be achieved.
A Scottish Government spokesman said: "Positive progress has been made towards delivering the projected savings of £1.1bn by 2026 - with approximately £880 million of recurring savings already secured.
"At the SPA Board meeting on March 26, the Chief Constable confirmed the £1.1bn savings target would be delivered two years early."