Andrew Swan says Manitoba's position includes the results of public hearings which took place in 2009 that heard overwhelming support from Manitobans for outright abolishment or reform.
The motion states the Senate too often serves partisan objectives rather than public interest and that any confidence Manitobans had in the upper house has been shaken due to the events of the past year.
In August, Manitoba made a submission, known as a factum, which addressed the constitutional questions posed by the federal government to the Supreme Court of Canada.
The province's position was that Parliament does not have the constitutional authority to enact significant unilateral changes to the structure of the Senate or to the selection of its members.
A vote was expected in the legislature later today.
"In this province, we abolished the upper house in 1876," Swan said. "We're calling on the Government of Canada to start negotiations with the provinces. It is time to get started on abolishing the Canadian Senate."