A campaign to raise the necessary money has so far raised more than £ 240,000 (around € 280,000), but parliamentary rules prohibit the money from being used for Big Ben.
"January 31st is a significant moment in our history as the United Kingdom leaves the European Union and regains its independence", Johnson's office said in a statement setting out its plans to mark Brexit - a moment which will be celebrated by some and mourned by others in a country still divided on the issue.
Stand Up 4 Brexit's "Big Ben must bong for Brexit" campaign had raised £152,470 of its £500,000 target from nearly 10,000 donors on the GofFundMe website by Friday morning.
But Brexiteer MP Mark Francois said the Prime Minister would be mad to back down now.
"January 31st is a significant moment in our history as the United Kingdom leaves the European Union and regains its independence", a government statement said.
"I think that will happen, yes, it's hard to say when", said Mr Verhofstadt.
"We have been impressed by members of the government and junior ministers who have quietly got on with driving real change within their departments and delivering on the PM's priority to level up our country", the source continued."It doesn't take two weeks to put a temporary floor in and attach a clapper to a bell".
Johnson raised his eyebrows on Tuesday when he said replacing the deal with a "Trump Deal" was "a great way forward".
Johnson's office, which has spent the week trying to cover up the prime minister's blunder, appeared to accept that the bell won't ring, saying instead that a clock will be projected onto the walls of the prime minister's office in Downing Street as the country counts down to Brexit at 11 p.m on January 31.
An attempt by some MPs to enshrine these chimes into law was dismissed in the U.K.'s Parliament last week.
But a spokesman said there would not be a flag-lowering ceremony. The British government plans to mark the occasion with a series of upbeat events.
This immediately kicked off a Westminster blame game with the committee blamed Boris Johnson for failing to check it was possible to sound Big Ben before encouraging the public to donate money.
Johnson said he was debating a "bung a bob for a Big Ben bong" fund that people could contribute to - the AP reported that "bung" is an informal term for toss and "bob" is informal for shilling.
"Our focus is on the events that the Government are now working on".
The new Speaker of the Commons, Lindsay Hoyle, who chairs the commission, said, "you're looking at £50,000 a bong".