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Mark Carney, who has served as the governor of the Bank of Canada and the Bank of England, speaks at the Sustainable Finance conference, on Nov. 28.Adrian Wyld/The Canadian Press

Talks with former Bank of Canada governor Mark Carney have broken off and he’s not joining the Liberal government, Finance Minister Dominic LeBlanc says.

Mr. LeBlanc, a New Brunswick MP, told Brunswick News that “Carney is not an option,” and “that discussion has concluded,” going on to say he has been given assurances by Prime Minister Justin Trudeau that the finance portfolio belongs to him.

Mr. LeBlanc was named Finance Minister after Chrystia Freeland resigned Monday from Mr. Trudeau’s cabinet. The Globe and Mail, citing three sources, reported that she decided to step down after Mr. Trudeau told her in a Zoom call on Friday that she was going to be replaced by Mr. Carney.

A cabinet shuffle is still expected, however, and could come as early as Friday, a government source told The Globe.

The Globe is not identifying the source who was not authorized to discuss cabinet deliberations.

Mr. Trudeau is expected to replace Mr. LeBlanc at Public Safety, one of his prior responsibilities, and will also fill gaps being left by a slew of other cabinet ministers who have already announced they are not running again. The most recent is Housing Minister Sean Fraser.

On Sunday, a senior Liberal source said Toronto MP Nate Erskine-Smith is expected to be promoted to cabinet in the coming shuffle, with housing a likely portfolio. He has previously said he won’t seek re-election but is now expected to stay on the ballot in a bid to keep his riding Liberal in the next campaign.

The Globe is not identifying the source who was not authorized to discuss the matter.

More MPs are adding their names to the list of those who think Mr. Trudeau should not run again.

Brunswick News also reported Wednesday that MP Jenica Atwin says Mr. Trudeau should quit and she wouldn’t run again for the Liberals if he stays. Ms. Atwin was recruited by Mr. LeBlanc to cross the floor from the Greens to the Liberals in 2021.

At least 15 Liberals have publicly called for Mr. Trudeau to resign, including Ms. Atwin, Brendan Hanley, Yvan Baker, Helena Jaczek, Patrick Weiler, Wayne Long, René Arseneault, Chad Collins, Sean Casey, Anthony Housefather, Francis Drouin, Ken Hardie, Serge Cormier, Alexandra Mendès and Ken McDonald.

Mr. Long, also a New Brunswick MP, circulated a letter Wednesday urging his colleagues to speak up and add their voices to his call that Mr. Trudeau must go.

“The time for loyalty at all costs, for quiet hand-wringing and polite whispers behind closed doors, has passed,” he wrote. “This isn’t just about one man – it’s about saving our party from a historic defeat.”

Along with the internal dissent by MPs, the Trudeau Liberals have been behind Pierre Poilievre’s Conservatives by double-digit poll numbers for more than a year.

The Conservatives and the Bloc Québécois demanded this week that Mr. Trudeau call an election, with NDP Leader Jagmeet Singh saying the Prime Minister needs to resign.

Ms. Freeland’s sudden departure Monday morning, just hours before she was to deliver the fall economic statement, knocked official Ottawa off course, including requiring the statement to be delayed for several hours, and a last-minute swearing-in of Mr. LeBlanc as Finance Minister later that day.

Liberal Christmas parties, however, proceeded as scheduled, and on Tuesday night, Ms. Freeland was mobbed as people lined up to get selfies with her.

In a speech to the gathering, Mr. Trudeau alluded to the party infighting and loss of Ms. Freeland as finance minister.

“It has been an eventful couple of days. It has not been easy,” he said. “Like most families, we sometimes have fights over the holidays and sometimes like most families we work our way through it.”

He did not address whether he will remain party leader.

Mr. Carney has held repeated talks with the Liberals about joining their ranks over the past several months.

In July, Mr. Trudeau acknowledged that he had asked Mr. Carney to join the government. At that time, Mr. Carney turned down the offer but, in September, he agreed to head a Liberal Party task force on economic growth, seen by many as a rebuke of Ms. Freeland.

Ms. Freeland was told by Mr. Trudeau on Friday during the Zoom call that Mr. Carney was coming into government, and she would be given a portfolio overseeing Canada-U.S. relations. The position would not be backed by a government department nor would she have any statutory authority to implement any policies, The Globe reported.

Ms. Freeland rejected the offer, and in resigning Monday, put out a sharply worded statement saying she and Mr. Trudeau had been at odds for “the past number of weeks.”

She laid out a specific tension: Her belief Canada needed to be better prepared to financially manage the possibility of incoming president-elect Donald Trump going through with his tariff threats versus what she called “costly political gimmicks.”

Mr. Carney has not responded to questions from The Globe about the offer of becoming finance minister.

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