In a bid to keep the £48.3 million building on budget, Hadid has already had to ditch a proposed aluminium-sheet cladding system, reduce the thickness of the 'interior lining' and 'adjust' the size of the windows on the north and south facades.
The Iraqi-born architect, who recently missed out on the Stirling Prize with her Phaeno Science Centre in Germany, has also agreed to add two new columns to reduce the amount of supporting steel work and investigate alternative materials 'which offer cost savings'.
The building will now be clad in a proprietary zinc cladding system attached to a steel supporting structure.
According to a Glasgow City Council report which is going to committee on Friday (27 November): '[The] tender price for the building is above the allocated budget [and contractor] HBG Construction, the project architect and engineer are exploring opportunities to reduce the cost of the building as part of the stage one development.'
Meanwhile it has also been revealed that Bovis Lend Lease - one of only four contractors invited to tender for the job - decided to withdraw from the selection process blaming 'questions of design risk'.
The purpose of Friday's meeting is to approve the appointment of HBG Construction to carry out phase one of the project, which is still expected to be handed over in September 2008.
Councillor John Lynch, the council's executive member for culture and leisure, is confident the museum will still be a unique and iconic building.
He said: 'The changes to the design specifications will not diminish the outstanding beauty of Zaha Hadid's plans, but will ensure that cost control and value for money are to the fore.'