Amazon could rival the nation's big banks in as few as five years, capitalizing off its digital prowess and massive consumer base, according to a Bain & Company report.

"We could imagine Amazon's banking services growing to more than 70 million U.S. consumer relationships over the next five years or so — the same as Wells Fargo, the third-largest bank in the US.," wrote Bain's Gerard du Toit and Aaron Cheris. "Although many retail bankers and observers have pegged the nimble fintech start-ups as the likely disrupters, it has become clear that established technology firms pose a bigger threat."

Pushing customers toward a co-branded banking account also allows Amazon to cut down on transaction costs, Bain said.

Amazon could – according to Bain calculations – avoid more than $250,000,000 in credit card interchange fees every year if finds a bank willing to partner on checking accounts.

Source: Bain & Company

The e-commerce giant is in early talks with financial institutions including J.P. Morgan Chase. The project is aimed at younger customers and those without banking accounts, The Wall Street Journal reported Monday. That focus on a younger demographic may be key, Maureen Burns, partner at Bain & Company and a leader in its financial services practice told CNBC.