After Amazon announced its plan to acquire Whole Foods, the market started buzzing about the internet giant's next potential acquisition.

Then there's big-box retailer Wal-Mart, which has also been on a buying spree of late.

The two companies are competing for the same shoppers, as one attempts to step into the other's core area of focus — Wal-Mart growing its e-commerce platform, and Amazon expanding a portfolio of real estate.

All things considered, location intelligence company Foursquare, which is able to track where users are "checking in," has made a prediction of the retailers it believes Wal-Mart and Amazon might go after next.

"We can make informed recommendations about which brands Amazon and Walmart should target next using our proprietary data-driven insights," Foursquare CEO Jeff Glueck said in a blog post Wednesday.

Foursquare analyzed foot traffic trails from more than 2.5 million Americans, anonymously, between January 2016 and June 2017.

The acquisition that makes the most sense, for both companies, is department store chain Nordstrom, Glueck said. This prediction comes as the Nordstrom family has been searching for its own buyer, hoping to take the company private.

A representative from Nordstrom didn't immediately respond to CNBC's request for comment on this story.

Nordstrom shoppers are about two times more likely to shop at Whole Foods than the average consumer, according to Foursquare, so that's where a deal with Amazon begins to make sense. "An Amazon-owned Nordstrom chain would deepen Amazon's relationships with its expanding core base," Glueck said.

Source: Foursquare

Meanwhile, Wal-Mart might want a company like Nordstrom in its portfolio to capture more millennial shoppers; Nordstrom shoppers are, on average, 55 percent less likely to shop at Wal-Mart than other American consumers, Foursquare found.

Following a similar trend of Wal-Mart acquiring more millennial-friendly apparel brands ModCloth and Bonobos, "A Nordstrom purchase would help Walmart further develop the expertise to combat Amazon," Glueck said.

Another retailer that would make sense for both Amazon and Wal-Mart to consider acquiring is Warby Parker, Foursquare says.

In this deal, Amazon would learn from Warby's "showroom experiments" in the brick-and-mortar world, while Wal-Mart could "lure Warby ladies into its big-box stores."

In picking one unique partnership for both Amazon and Wal-Mart, Foursquare has suggested the internet giant acquire Lowe's and the big-box retailer look to Ulta Beauty.

"Amazon loves to win, so imagine what would happen if they cut prices and sacrificed margin to compete for marketshare, further growing their share of DIY homeowners," Glueck wrote about Lowe's working with the e-commerce conglomerate.

Meantime, in Ulta Wal-Mart would find a loyal customer base.

"Our data also shows that there are a wide swath of Ulta shoppers who are just as likely as the average consumer to visit Walmart, whereas another cosmetics brand — Sephora, for example would be less of a willing convert to an Ulta/Walmart store," Glueck said.

"Walmart likely covets Ulta's customer base."

It's true, beauty marks a bright spot in retail today as apparel companies and other specialty names are struggling to keep pace with change.

And home improvement companies Home Depot and Lowe's have already seen their stocks take somewhat of a hit on fears that they aren't "Amazon-proof."

Notably, in the spring of 2016, Foursquare CEO Glueck told CNBC he was predicting Chipotle's comparable sales would fall by 29 percent in its first quarter, based on user data tracked via the company's app. Two weeks later, Chipotle reported sales dropped 29.7 percent.

Amazon, Wal-Mart, Warby Parker, Lowe's and Ulta did not immediately respond to a request for comment.

Read the full post from Foursquare.