Once upon a time, Amazon.com (NASDAQ: AMZN) had its own mobile credit card reader just like Square's (NYSE: SQ). Even though it undercut Square's pricing, by offering a promotional rate one percentage point lower than its standard 2.75% cut on each transaction, Amazon Register never made a dent in the market.

However, Amazon could be going after Square's newfound success with its Cash App and the financial services it offers consumers and businesses. The retail giant is reportedly in talks with banks to develop a checking account-type service to millennials and the underbanked. That's a key market for Square, and Amazon's entry has a much better chance at a favorable outcome than Amazon Register.

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Bringing technology to banking

Square believes it can make traditional banking services more accessible by using technology. Square Capital, its small-business lending arm that launched in 2014, collects data on merchants -- such as transaction size and volume and inventory information -- to offer loans to store owners banks wouldn't usually touch. The company is thinking about expanding Square Capital to consumer loans.

Cash App is starting to look a lot more like a checking account, too. Users can receive a direct deposit from their employer through the app, and they can spend down their balances using a debit card issued by Square. On the fourth-quarter earnings call, Square CEO Jack Dorsey said it's focused on serving the underbanked, and the surging use of Cash App in the past year indicates that it's paying off.

To be sure, Square has very successfully injected technology and data science into traditional banking services. Amazon has also accomplished the same thing across numerous industries including retail, advertising, and movie and television production. And Amazon is also working to use its proficiencies in the health insurance and delivery and logistics industries. But Consumer banking services seems to be next on the list for Amazon, according to a report from The Wall Street Journal.

Amazon has already had some achievements in the financial services realm. The company introduced Amazon Lending in 2011 to offer small-business loans to merchants using its marketplace to sell goods. As of last summer, it's doled out over $3 billion in loans.

Square Capital is quickly catching up to Amazon Lending in terms of volume. It's now originated nearly $2.5 billion in loans as of the end of 2017.

Amazon could stop Square's next move in its tracks

As Cash App grows in popularity, the next move for Square is to exploit its users' data in order to add new financial services like consumer loans. It can also employ that data to target advertising for its merchant partners.