People may be able to donate money towards the cost of making Big Ben chime when the UK leaves the EU, Boris Johnson has said.
The prime minister said getting the famous bell to ring at 23:00 GMT on 31 January would cost £500,000, but some form of crowdfunding might be possible.
Big Ben has only rung on a few occasions since refurbishment of the tower housing it began in 2017.
A bid to get the bell-ringing enshrined in law was dismissed last week.
An amendment to the PM's Brexit bill, which would have required it to chime on Brexit day, was not selected for a vote in the House of Commons.
"We're working up a plan so people can bung a bob for a Big Ben bong, because there are some people who want to," Mr Johnson told BBC Breakfast.
"Because Big Ben is being refurbished, they seem to have taken the clapper away, so we need to restore the clapper," he added.
"And that is expensive, so we're looking at whether the public can fund it."
The PM's official spokesman said there was not a "specific government fund" to meet the costs, but added: "If the public wants Big Ben to bong and the money is raised, then that is great.
"We will make sure that - whatever happens in regard to Big Ben's bongs - January 31 is properly marked. It is a significant moment in our history."
The House of Commons Commission, which manages the parliamentary estate, said the extra spending could not be justified, but it would listen to MPs on the matter.
The body heard that for the bells to chime, a temporary mechanism used on Remembrance Sunday and New Year's Eve would have to be restored to the Palace of Westminster's Elizabeth Tower, and a temporary floor of the belfry installed.
Costs for this work, alongside testing and ringing the bell, were estimated at approximately £120,000. In addition, existing restoration works would be delayed by two to four weeks, at a cost of £100,000 per week.
Authorities said the £320,000 minimum cost could therefore rise to £500,000 - the figure cited by the PM.
Would Brexit bongs cost £500,000?
The House of Commons Commission's estimate is made up of two separate costs - bringing back the bonging mechanism and installing a temporary floor, and the cost of delaying the conservation work.
On the former, the commission says the floor in the belfry has been removed - work that began on 2 January in order not to interfere with New Year's Eve.
The reconstruction work on the floor is likely to be significant, involving resurfacing and waterproofing.
The Commons has ruled out getting this done by 31 January, which is why a temporary floor would need to be installed and then removed - at a significant cost.
Commons Speaker Sir Lindsay Hoyle said: "The Commission believes it is important to weigh up the costs this would involve if Big Ben is to chime on 31 January.
"You are talking about £50,000 a bong. We also have to bear in mind that the only people who will hear it will be those who live near or are visiting Westminster."
However, Brexit Party leader Nigel Farage questioned the £500,000 figure, and accused the commission of "obstruction".
In an article for the Telegraph, he wrote: "It tolled on New Year's Eve, on Remembrance Sunday and on Armistice Day.
"Did this cost £500,000 on each occasion? I would love to know the answer."
Clock restoration expert Paul Kembery said a temporary platform and electric motor had been used to chime the bell on Remembrance Sunday and New Year's Eve.
But he told the BBC's Victoria Derbyshire programme that with only just over two weeks to go, there was probably not enough time to put both back in, even if the public raised the required funds.
Brexiteer Mark Francois, one of the Tory MPs behind the bid to legislate for the Brexit day bongs, has said it would be "inconceivable" if Big Ben did not sound to mark the occasion.
"As we leave at a precise specified time, those who wish to celebrate will need to look to a clock to mark the moment," he added.
But Labour MP David Lammy said £500,000 was a "huge amount of money to waste on jingoism".
"I am not fussed about whether Big Ben bongs on Brexit day [...] what I care about is the £130bn and counting that leaving the EU has already cost," he tweeted.