The Joint Committee on the Palace of Westminster will on Thursday recommend that MPs move into the nearby Department of Health with peers going to the Queen Elizabeth II Conference Centre, a committee source said.
According to The Times, Prime Minister Theresa May is set to back the call, increasing the likelihood that it will happen, but it will still be subject to a parliamentary vote.
The committee will recommend that the move takes place between 2022 and 2028, the source said.
A study by Deloitte last year highlighted the appalling condition of the Palace of Westminster, with potentially deadly fire risks, collapsing roofs, crumbling walls, leaking pipes and large quantities of asbestos.
The committee of MPs and peers is set to back one of the options set out in the study - that there should be a full decant, estimated by Deloitte to cost between £3 billion to £4.3 billion - with the most likely figure £3.5 billion.
If politicians refuse to leave the building, patching it up to basic standards will take around 32 years and could cost between £4.9 billion and £7.1 billion, the June 2015 study said.
A Downing Street spokeswoman said: “We are awaiting the report and will respond in due course.”