Boris Johnson has suggested Parliament could move to York while the Palace of Westminster undergoes renovation.
In a letter, the prime minister said the government was considering establishing a hub in the northern city and “it would therefore make sense to consider this as a potential location”.
Plans to move MPs out of Westminster are being reviewed due to the impact of coronavirus on public finances.
The move, if it happens, is expected to take place around 2025.
Other possible London locations proposed by Mr Johnson in the letter to David Goldstone and Sarah Johnson, who are overseeing the restoration project, include Richmond House, the QUII (Queen Elizabeth II Centre) and City Hall.
Mr Johnson said that the case for both Houses staying in place should also be considered.
In his letter, seen by the BBC, the prime minister said: “We all have a responsibility to protect the Palace of Westminster as a functioning building and as the iconic UNESCO World Heritage site that is the home and symbol of our democracy.
“The current situation is unsustainable given the serious risk of a major fire and the need to upgrade the services throughout the building.”
Mr Johnson added that “costs are obviously a major driver” in the review but said other factors including disruption to Parliament’s work, the timelines for delivery, heritage benefits and fire safety, should be considered.
“We should also move as quickly as possible, both because of the risks associated with the current state of the building and the need to provide certainty on the way forward and thereby minimise disruption to our business,” he added.
The letter also said that the location of Parliament was a constitutional issue and that the views of parliamentarians would need to be considered carefully.
The review into the project and the potential move is expected to report its recommendations in the autumn.
Before Parliament voted in 2018 to approve the renewal works, which would entail decanting the whole building for at least six years, MPs had pushed rival plans that would have seen only a partial vacating required. This would have forced builders to work around the Commons schedule.
A recent report by the National Audit Office (NAO) stated that the £4bn cost previously reported for the restoration project was likely to be a “median” figure, with the final outlay expected to be higher.