Is Popeye giving up spinach for a Wimpy burger? Not quite, but Burger King just might be willing to chow down on some Popeye's Louisiana Kitchen (NASDAQ:PLKI).

On Monday, a rumor made the rounds that Restaurant Brands International (NYSE:QSR), the parent of Burger King and Canadian coffeehouse Tim Horton's, had approached the fried-chicken joint about a merger, though a price still had to be agreed upon. Considering the banner quarter the fast-food operator reported at the same time, a takeover deal isn't such a stretch, and the sources for the rumor say Restaurant Brands has been eyeing other potential candidates as acquisition targets, as well.

Built for growth

It was the strength of each of Restaurant Brands' individual restaurants that had company franchisees building more stores. The company added 32 new locations in 2016 compared to just one the year before, though other fast-food outlets have also started building out their chains again. Wendy's just announced its preliminary full-year results, and it says it added almost 150 restaurants last year, the largest number of new openings since 2005.

Systemwide sales at Tim Horton's grew 2.4% in the fourth period and were up 8.5% at Burger King, as comparable sales rose 0.2% and 2.8%, respectively.

The recovery in industry same-store sales is helping to drive the rebuilding program. Restaurant Brands CEO Daniel Schwartz said it signed a number of development agreements for the Burger King brand in the U.S., which, he notes, "will fuel further opening and remodels in the country for many years to come."

Burger King has about half the number of McDonald's (NYSE:MCD) restaurants in the U.S. and Canada. Where the Golden Arches sports around 15,000 locations, Burger King has only 7,400, but Schwartz says "there is no reason that the Burger King brands shouldn't be growing at an accelerated pace in the U.S."

A close up of a Burger King Whopper sandwich.

Image source: Restaurant Brands International.

According to Reuters, which first reported the alleged takeover discussions between Restaurant Brands and Popeye's, the rationale behind such a deal would be to bring the latter's Louisiana-style fried chicken and buttermilk biscuits to a broader global audience using Restaurant Brands' international muscle.

Popeye's, though, has been on a building spree itself, opening 52 restaurants in the U.S. in the fourth quarter and 37 internationally, bringing its total new restaurant openings for the year to more than 200. It has a total of 2,688 restaurants in operation, more than three quarters of which are in the U.S.

A tough merger to swallow

While both Restaurant Brands international and Popeye's refused to comment on the merger rumors, and though the latter's stock soared initially on the report before coming back down when nothing materialized right away, there are analysts who are doubtful the story is real. Not in the sense it was "fake news" like the press release purportedly issued last week by McDonald's saying it was buying out Chipotle Mexican Grill for $570 per share, but rather they didn't believe Restaurant Brands was ready to make an acquisition since it had yet to fulfill the promise of its purchase of Tim Horton's.

A cup of Tim Horton's coffee being poured surrounded by coffee beans.

Image source: Tim Horton's.

When Burger King bought Canada's largest coffee and donut shop for $11 billion in 2014, the idea was that it would be able to spread that signature combination internationally while letting the burger joint begin selling packaged goods in supermarkets.

That growth, though, has been slow in coming. Today, there are only about 100 more Tim Horton's operating than there were at the time of the acquisition. Now, it supposedly wants to take on another fast-food chain and grow it globally, too.

Of course, this isn't the first time Restaurant Brands was supposedly interested in buying Popeye's Louisiana Kitchen. The New York Post says the burger joint walked away from a proposed buyout of its rival "a few months ago," and its source says that, although talks may have started up again since, it wasn't likely.

While Burger King, Tim Horton's, and Popeye's are all doing better for themselves, McDonald's stumbled in the recent quarter, indicating the fast-food industry is still on shaky feet, like much of the rest of the dining category. Another big deal, such as a Popeye's buyout, probably isn't on the menu.