Instead, as the world's largest retailer pushes forward in the category — which makes up roughly half of its sales — Amazon is reportedly eyeing a bigger piece of the action.
According to The Wall Street Journal, the e-commerce giant plans to open convenience stores that sell milk, produce and other consumables, as well as drive-up destinations where shoppers can have their orders brought to the car.
People familiar with the strategy told the newspaper that shoppers could use their smartphones or screens scattered around the shops to place their orders. The drive-up service, which replicates Wal-Mart's successful online grocery strategy, would be designated for shoppers who place their orders ahead of time.
A spokeswoman for Amazon told CNBC the company does not comment on rumors or speculation.
The Journal story comes just days after Wal-Mart reiterated its commitment to its online grocery business. When Wal-Mart's online sales growth picked up in the fiscal second quarter, growing roughly 12 percent, management attributed part of the acceleration to this service. Not only has it brought new customers into its ecosystem, but these shoppers tend to grab additional items when they pick up their orders, the company has said.
This capability has been rolled out to 80 markets and 500 stores, and will be in 100 markets and 600 stores by year's end.
Though digital grocery sales have been slow to take off for both Amazon and the industry overall, as shoppers have been reluctant to allow someone else to choose their produce, Cowen and Co. analyst John Blackledge says there's huge potential for the e-commerce giant to grab a larger share of spending.
Online groceries now account for about 2 percent of total grocery sales within the United States, according to IBISWorld.
In a report on the grocery industry earlier this year, Blackledge said Amazon's food and beverage revenues fell shy of earning it a slot in the top 20 grocery retailers. However, as shoppers become more comfortable with the idea of purchasing groceries online, Amazon has emerged as a name that they trust, his research has found. As such, Blackledge estimates Amazon will become the seventh-largest food and beverage retailer in the U.S. by 2021.
"The U.S. food and beverage grocery market has reached a tipping point, in our view," he said in the report.
Grocery could signal a big opportunity for Amazon, as food needs to be replenished frequently. However, its Fresh service is only available in a handful of markets, and comes at an additional cost to Prime members. Whereas an annual Prime membership is $99, Amazon Fresh tacks on another $14.99 a month.
Amazon has been dipping its toe into bricks-and-mortar stores, including a bookstore in its home market of Seattle and 25 pop-up locations around the U.S.