Big Ben is being renovated, but the PM this week suggested a fund be set up to make it chime at 23:00 on 31 January. But the MPs' group responsible for such undertakings doubts this would be feasible given the time constraints.
The House of Commons Commission estimates that getting the bell to ring would cost between £350,000 and £500,000, Presstv Reported.
To do so would necessitate reinstalling the chiming mechanism and installing a temporary floor, which would result in delays to the conservation work.
The commission argues the estimated costs could not be justified, and questions the idea that public donations should cover them.
Boris Johnson was the one who had "fired the starting gun" on the campaign by suggesting public donations during his BBC Breakfast interview on Tuesday.
Responding to a question in Parliament from Mr Francois, Sir Paul Beresford - a member of the commission - said the cost of ringing the bell on New Year's Eve and Remembrance Sunday in 2019 had totalled £14,200.
"The striking of Big Ben on these occasions was co-ordinated around the planned works so as to minimise the impact on the project costs and to ensure it did not result in any delay," Sir Paul said.
"If the project team are required to strike the bell with less notice, the costs would substantially increase due to the unexpected impact on the project schedule."
Downing Street has said the chiming of Big Ben is "a matter for the House" of Commons.
Commons Speaker Sir Lindsay Hoyle, who is chairman of the Commons Commission, said: "You are talking about £50,000 a bong."