The MP was convicted last Friday.
Davies, 51, admitted to two charges relating to creating false invoices for £700 worth of photographs.
The politician could have made the claim legitimately under a different process. His case was adjourned for sentencing at a future date at Southwark Crown Court.
The figure needed to trigger a by-election is yet to be confirmed but it is thought around 5,300 names would be required.
Davies had admitted to one charge of providing false or misleading information for allowances claims, and one of attempting to do so.
A spokeswoman for the Speaker's Office said: "As soon as the court has formally informed Mr Speaker that sentencing has taken place, procedures under the Recall of MPs Act 2015 require him to write to the returning officer in Mr Davies' Brecon and Radnorshire constituency.
"Once the letter has been sent, Mr Davies is subject to the recall petition process and it will be for the returning officer to make the arrangements for the petition.
"The recall petition will be open for signing for six weeks," the spokeswoman added.
"If at least 10% of the electorate in the constituency sign the petition, the MP will lose his seat and a by-election will be triggered."
Once called, a recall petition should be available to be signed at up to ten locations open from Monday to Friday between 0900 and 1700, with "reasonable provision" given for signing at other times.
|Liberal Democrat||James Gibson-Watt||12,043||29.1||+0.8|
|Plaid Cymru||Kate Heneghan||1,299||3.1||-1.3|
|Liberal Democrats||Kirsty Williams||15,898||52.4||+9.3|
|Plaid Cymru||Freddy Greaves||1,180||3.9||−2.8|
|Liberal Democrats hold||Swing||+8.6|
8,895 people are talking about this
Though Hartley-Brewer’s intervention, as is so often the case, isn’t based in the world of facts.
Firstly, no email address can be used repeatedly.
For your name to be counted, each person has to click a verification e-mail link, which can only be used once.