The number of letters already sent in is said to be “substantial”, according to Sky News.
Sir Graham Brady, chair of the 1922 Committe – a group of backbench MPs that oversees the election of party leaders – is reportedly on holiday at the moment but will receive the letters when he returns on Monday.
Rebel Conservative MPs are apparently urging colleagues to submit letters expressing no confidence in Ms Truss to give Sir Brady a mandate to change the rules of the leadership election process.
Rules could be changed to raise the number of supporters required to get on the first ballot of a leadership race from 20 to 100. This would mean that only the most popular candidate would make it past the first step and would effectively be coronated as leader of the Conservative party.
MPs have speculated that a Rishi Sunak-Penny Mordaunt joint ticket could get past the 100 vote threshold.
They also believe that if enough letters go in then Sir Brady would have the authority to go to Ms Truss and tell her to resign.
One MP told The Times that Conservatives could start to publicly demand Ms Truss’s departure on Monday.
The Daily Mail reported that MPs are privately sounding out colleagues ahead of an attempted coup to oust the prime minister.
A group of 20 or so “poppadom plotters” met over curry in Parliament’s Portcullis House to discuss how they could get rid of Ms Truss.
There have reportedly been discussions about asking former Tory leaders to sign a joint statement calling for Ms Truss to stand down.
“It’s not just about the survival of the government or even the Conservative Party,” one source said.
“People are suffering real world pain from the incompetence we have seen – I’ve got friends who cannot get a new mortgage. We have a duty to stop this and restore a basic level of competence.”
MPs discussed whether the cabinet or Sir Brady could be persuaded to tell Ms Truss her time was up, the paper reported.