At the same time, Duffy has sent a letter to the Speaker of the Senate, Noel Kinsella, requesting a medical leave of absence due to a heart condition.
Duffy and Wallin have both repaid money to the Senate after questions about their expense claims. Duffy repaid more than $90,000 in March with a personal cheque from Prime Minister Stephen Harper's former chief of staff. Wallin complied with a Senate order to repay more than $140,000, including interest, in September.
Both senators were subjects of damning forensic reports from the accounting firm Deloitte about inappropriate spending. Duffy is now being investigated by the RCMP over his Senate expense claims.
A Conservative notice of motion to suspend Wallin and Duffy will come from the government leadership in the Senate in its first meeting since the House was prorogued last June. The motion could be adopted immediately if there were unanimous consent from every senator, including Wallin and Duffy if they were present.
But it's more likely the motion would be put aside for 48 hours, as Senate rules require if there's no unanimity, and then debated at the Senate's next session on Tuesday. After a debate, the motion would be put to a vote that would require a simple majority to pass. The Conservatives have a majority in the Senate.
The idea of the motion was considered at a meeting of the Conservative caucus this week, senior Conservative sources tell CBC News. Apparently two options were explored. The first was to expel the senators altogether, a move that was ultimately deemed unlikely to stand up legally.
The second option was to suspend them from the chamber, meaning they would not be able to take their seats in the chamber or attend committees. A handful of Conservative were upset about what they viewed as a lack of due process, since neither Duffy or Wallin are facing any charges.
However, both Duffy and Wallin have been placed under administrative restrictions which bar them from undertaking outside travel on Senate business, other than trips between Ottawa and the provinces they have designated as their primary residences.
Senator Patrick Brazeau, who is also under investigation by the RCMP for his expense accounts, was suspended earlier this year by the Senate after he was charged for sexual assault in a separate matter. Days after his charge, the Senate voted unanimously to suspend him with pay, in a motion that stated in order to "protect the dignity and reputation of the Senate and public trust and confidence in Parliament, the Senate order a leave of absence."
It's expected that Brazeau's suspension, which was erased by the prorogation of Parliament, will be reinstated.