The Times claims to have seen a leaked report which claims that MPs will be relocated to the Department of Health offices in Whitehall while a multi-billion-pound refurbishment of the House of Commons and House of Lords begins in 2020.
Lords' peers will be transferred across Parliament Square to the Queen Elizabeth II Centre.
As the new temporary home for MPs, Richmond House, is held under an Islamic bond scheme, it forbids the sale of alcohol.
That will give authorities three years to transform the property into a functioning parliament. It is thought that the debating chamber will possibly be housed there.
More From This Section
The lease on Richmond House, where MPs are due to move, was transferred to finance an Islamic bond scheme two years ago. This means that it cannot be used for anything that is not sanctioned by Sharia law.
One of the terms agreed with the UK Treasury is that the sale of alcohol is forbidden, whereas at their current location in Westminster, MPs have the choice of 10 licensed bars and restaurants.
Devout Muslims cannot buy traditional government bonds because they pay interest. Sukuk, an Islamic alternative permit guaranteed returns if they are linked to rental payments.
Moving MPs and peers out of the Palace of Westminster will enable the building work to be completed quicker and more cheaply - in six years, costing between 3.5 billion and 3.9 billion pounds, the leaked report indicates.
A vote in Parliament on the recommendations is due after the ongoing summer recess.
The restoration and renewal unit of the British Parliament has said that since the UNESCO world heritage site's construction in the mid-1800s "many features have never undergone major renovation".
"The roofs are leaking, asbestos is present throughout, corrosion has occurred in gutters and downpipes and internal plumbing regularly fails, causing visible and sometimes irreversible damage to the Palace's carved stonework ceilings and Pugin-designed historic interiors," it says.