The Canadian federal government and provincial Ontario governments received 1.7 percent of Chrysler two years ago as part of a bailout that also provided $1.7 billion in loans to help the Detroit company survive.
Chrysler, already controlled by Fiat, recently paid back the last of the money it borrowed from the Canadian and American governments. Fiat then began the process of buying the shares owned by the U.S. government.
Chief executive Sergio Marchionne joined Canadian Finance Minister Jim Flaherty at a Chrysler Canada casting plant in Toronto on Monday to announce the loan repayment.
Marchionne said that he and Flaherty discussed buying Canada's shares and said they are quite willing to consider purchasing them.
Unlike with the shares owed by the U.S. government, the company has no right to compel the Canadian government to sell.
Flaherty said Ottawa will wait to see how the stock transfer process unfolds in the United States before deciding whether Canada will also sell its shares.
The Turin, Italy-based automaker said Friday it will buy the U.S. government's six percent stake in Chrysler under a process that was put in place in 2009 when Chrysler virtually shut down while in bankruptcy court.
Fiat initially received a 20 percent stake in Chrysler in 2009 for providing Chrysler with management expertise and technology.
Since then Fiat has been increasing its holdings in Chrysler and will soon control more than half of the company.
Fiat has helped change the corporate strategy of Chrysler, brought new fuel-efficient vehicles quickly to market and made the company cut costs and operate more efficiently.
The future looks brighter for the company, which has cut thousands of jobs in the United States and Canada in its bid to survive bankruptcy.
In Canada, the company employs 9,000 people and has major assembly plants in Windsor, a southwestern Ontario border city, and Brampton, a community northwest of Toronto.