Grubhub's (NYSE:GRUB) stock popped on Jan. 8 after The Wall Street Journal claimed that the food delivery company was mulling a potential sale. However, most of those gains faded the following day after Grubhub denied the rumors.

Grubhub stated that it "unequivocally" isn't running a sale process and that there were "currently no plans to do so." But this isn't the first time we've heard buyout buzz about Grubhub, which shed roughly a third of its value over the past 12 months amid brutal competition -- and it probably won't be the last.

Therefore, investors should still be familiar with Grubhub's rumored suitors to weigh the possibility of a future takeover. Here are three that people are talking about:

Grubhub's mobile app.

Image source: Grubhub.

1. Walmart

The New York Post recently claimed that Walmart (NYSE:WMT) could buy Grubhub to strengthen its online grocery delivery service, which the retailer cited as a key driver of its 41% annual e-commerce revenue growth in the U.S. last quarter. The report cited Britain Ladd, an ex-Amazon (NASDAQ:AMZN) executive and supply chain consultant, who claimed to have spoken with Walmart's insiders about the issue.

A recent survey by TABS Analytics found that 29% of American internet users bought groceries online from Walmart in 2019, up from just 12% in 2015. During the same period, Amazon's share jumped from 14% to 36%.

Acquiring Grubhub would help Walmart keep pace with Amazon, and would complement its online grocery push in other markets like China, where it runs a growing online grocery joint venture with JD.com (NASDAQ:JD). Integrating Grubhub into Walmart's massive network of over 4,700 stores across the U.S. could also bolster the meal delivery platform's margins with economies of scale.

It could also solve Walmart's last-mile delivery challenges -- which it unsuccessfully tried to address with customer- and employee-assisted delivery plans -- with thousands of Grubhub drivers. That expansion could enable its unlimited grocery delivery plan, which costs $98 per year, to reach more shoppers across America.

2. Amazon

Amazon previously tried to compete against Grubhub with its Amazon Restaurant delivery services in the U.S. and the U.K., but it exited both markets in 2018 and 2019. It retains an investment in Deliveroo, a British restaurant delivery service that operates in over 200 cities worldwide but doesn't operate in the U.S.

Meanwhile, Amazon expanded its reach into brick-and-mortar grocers with its takeover of Whole Foods in 2017 and converted AmazonFresh -- its $14.99 per month grocery delivery service -- into a free perk for Prime members in late 2019.

An Amazon delivery driver.

Image source: Amazon.

Buying Grubhub would instantly make Amazon the second-largest meal delivery platform in America with a 30% share of the market, according to Second Measure. Amazon's scale would also lower Grubhub's operating expenses, and the addition of its meals to AmazonFresh could give it an edge against Walmart and other rivals.

Amazon could also merge Grubhub with Amazon Flex, the Uber-like delivery service it launched in 2015. Amazon could also easily blend Grubhub into its broader digital ecosystem since it's already integrated into Echo devices as an Alexa skill.

3. Yum Brands

Yum! Brands (NYSE:YUM), the parent company of KFC, Taco Bell, and Pizza Hut, bought a 3% stake in Grubhub for $200 million two years ago. Grubhub starting delivering meals for KFC and Taco Bell after that investment.

Yum's initial investment in Grubhub shed significant value and throttled its earnings growth throughout fiscal 2019. However, acquiring a majority stake in Grubhub could enable it to restructure the whole company, drop all of Grubhub's other customers, and convert its entire fleet of drivers into dedicated couriers for its core brands.

That unified fleet of drivers would not only bolster KFC and Taco Bell's delivery capabilities but also replace Pizza Hut's part-time delivery drivers. Pizza Hut already launched a pilot program for Grubhub deliveries in over 700 stores in 2019, which suggests that Yum could significantly cut costs by replacing its own drivers with Grubhub's.

The bottom line

Investors should never buy a stock based on buyout buzz alone. Grubhub remains a troubled company that lost its market-leading position to DoorDash and posted decelerating revenue growth with plummeting earnings over the past year.

Aggressive price wars and shifting regulations regarding "gig economy" workers also cast a dark cloud over the entire food delivery market. Meanwhile, interested suitors could simply wait for Grubhub's stock to tumble even further before swooping in with an eleventh-hour offer.

Despite these issues, investors should be aware of the meal delivery market's dynamics, and understand that Grubhub could still be a valuable target for companies like Walmart, Amazon, and Yum Brands in the future.