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Burger King may be the home of the Whopper, but Canada may be the new home of Burger King.

The restaurant operator said on Sunday that it was in talks to buy Tim Hortons, the Canadian doughnut-and-coffee chain, in a potential deal that would create one of the world’s biggest fast-food businesses.

If completed, the deal would mean the burger giant’s corporate headquarters would move to Canada, raising the specter of yet another American company switching its national citizenship to lower its tax bill.

Under the expected terms of the deal, Burger King would create a new corporate parent that would house both chains, which would be operated independently. Together, the two companies would have a market value of more than $18 billion.

An agreement could be reached as soon as this week, a person briefed on the matter said.

Though the two companies are expected to argue that a merger would bring a host of strategic benefits, it would nevertheless count as a so-called corporate inversion. Many American companies have looked toward taking over foreign companies, and then moving their headquarters abroad, to lower their overall tax bill.

Inversions have become increasingly popular, though the practice has come under fire from Washington as the Obama administration and lawmakers have complained that companies that do so are unfairly — though legally — cutting their tax bills. The practice gained new prominence when Pfizer, one of the biggest names in corporate America, pursued a takeover of AstraZeneca in an effort to find a lower tax rate in Britain.

Treasury Secretary Jacob J. Lew recently said that the White House was weighing whether to take a harder line on inversions and that it had already identified potential ways in which it could block the corporate tax flight without having to rely on Congress to pass legislation.

Though most of the companies that have used inversions are big drugmakers like AbbVie, which makes the arthritis drug Humira but isn’t a household name, Burger King would be one that is highly visible to consumers. A company in a similar position, the pharmacy chain Walgreen, cited potential pressure from Main Street and Washington as a factor in forgoing a corporate relocation.

The American corporate tax rate is about 35 percent, while Canada’s is about 15 percent. But people briefed on the deal negotiations said that the main driver in the talks was not taxes. Burger King already pays a tax rate of roughly 27 percent, and would shave off only a couple of percentage points by moving to Canada, according to the people briefed on the matter.

And Burger King does not have a significant amount of cash held abroad, these people said. Companies often pursue inversions to gain access to their overseas cash without being hit by a big American tax bill.

One potential reason for the move may be to placate Canadian authorities. Deals in the country are governed by the Investment Canada Act, which allows the national government to block a merger if it is deemed to not be in the best interests of the country.

Given Tim Hortons’ status as one of the country’s iconic restaurants, a merger structure would allow it to remain Canadian. (The company was previously owned by Wendy’s, until it was spun off in 2006.)

The two companies are expected to argue that the deal makes sense because it would create a stronger competitor to McDonald’s and Yum Brands, the owner of Taco Bell and KFC. The combined restaurant operator would have about $22 billion in revenue and more than 18,000 restaurants worldwide.

Uniting Burger King and Tim Hortons would allow the company to grow faster worldwide, while creating a restaurant operator whose offerings span breakfast, lunch, dinner and snacks.

Coffee may be an especially important attraction for Burger King and its majority owner, the Brazilian investment firm 3G Capital. In Tim Hortons, Burger King would be getting a restaurant chain that is essentially synonymous with coffee in Canada.

As it marks its 50th year, Tim Hortons can claim a penetration into the Canadian fast-food market with few parallels. On a per capita basis, its 3,630 outlets in Canada would be about 36,000 shops in the United States, just over double the 14,700 McDonald’s has in its home market.

A takeover of Tim Hortons would be the latest twist in the 60-year-old life of Burger King. Started as a burger joint in Florida, it became a rival to McDonald’s. But it has never surpassed its rival, even after being taken over and reworked by private-equity investors multiple times.

Four years ago, 3G Capital bought control of the fast-food chain for $4 billion, focusing on a relentless cost-cutting initiative to help fix its troubled operations. It then brought Burger King back to the public markets two years ago by merging it with a publicly traded investment firm.

The company operates more than 13,000 locations, almost all of which are run by franchisees.