The £4bn multiyear restoration project on the Houses of Parliament is running behind schedule and could be delayed for several years, the Financial Times claim.
A third of MPs and hundreds of administrative staff are due to move out of during autumn so that work be completed on creating a temporary debating chamber and offices, while work on the palace is carried during the mid 2020s.
But so far temporary accommodation for those due to move is not ready or has not been found, as it has to be within the parliamentary estate for security reasons, the FT says, citing those working on the renovations.
This could result in restoration work being delayed and for every year the works are held up, the cost will increase by a reported £100m.
MPs voted last January to move out of the Palace of Westminster for six years rather than have contractors work around them, which would have been longer and more expensive.
Those residing in the House of Commons are due to move to the former department for health headquarters in Richmond House for around six years, while peers are set to relocate to the QEII Centre opposite Westminster abbey.
The historic buildings of Norman Shaw North, Norman Shaw South and 1 Parliament Street, next to the Houses of Parliament, currently house MPs and staff, but will have to be emptied for refurbishment so they can rehouse displaced MPs during modernisation work.
A spokesman for the Restoration and Renewal programme said: "This programme of works is already progressing, and we expect it to conclude in the mid-2020s so that the main restoration and renewal of the Palace of Westminster can progress”.