"Either could become acute at any time, causing the clock to stop - or worse."
Action is also needed to combat "severe metal erosion, cracks in the roof and other structural defects" in the Elizabeth Tower.
"There are major concerns that if this is not carried out within the next two to three years, the clock mechanism is at risk of failure with the huge risk of international reputational damage for Parliament," the report said.
"In the event of a clock-hand failure, it could take up to a year to repair due to the scaffolding needed."
The proposed 29 million pound "full refurbishment" would involve the clock being stopped for four months, and each of the four faces covered in turn a work was undertaken.
Officials admit it would cost only 4.9 million "to prevent the clock from failing", but they suggested the cost could rise to a cumulative total of £40 million if the underlying problems are not dealt with in one go.
The public purse is already facing a massive restoration bill of up to 7 billion pounds for the crumbling Palace of Westminster.