Calls from Brexiteers for the famous bell to chime on 31 January to mark the moment Britain leaves the European Union had been scuppered after the move was deemed to be too costly.
But in his first sit-down interview of the new year, the prime minister said the government was looking into a crowdfunding campaign to raise the £500,000 needed for the idea to go ahead.
He told the BBC: “We are working up a plan so people can bung a bob for a Big Ben bong.
“Because as everybody knows Big Ben is being refurbished they seem to have taken the clapper away, so we need to restore the clapper in order to bong Big Ben on Brexit night.
“That is expensive, so we’re looking at whether people can fund it.”
However the scheme appeared to unravel within hours, with Downing Street admitting that there was no plan for a specific government fund.
The prime minister's official spokesman said: "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 - 31 January is properly marked.
"It is a significant moment in our history."
The PM's spokesman added: "We are talking to the House at the moment. The House would need to agree to any proposal."
The House of Commons Commission dismissed the idea over financial issues during a meeting on Monday after it was revealed the original estimated cost of £120,000 had soared to £500,000.
Commons speaker Sir Lindsay Hoyle poured cold water over the plans, saying it would cost around £50,000 per bong if Big Ben were to chime at the end of the month.
"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."
The 315ft, Grade I-listed Elizabeth Tower which holds the bell and clock face is undergoing a £61m restoration, in which costs have already more than doubled.
Brexit Party leader Nigel Farage has claimed he is planning to throw a £100,000 party in Parliament Square with fireworks, bands and speakers to mark the UK’s departure from the EU at 11pm on 31 January.