JPMorgan Chase, Wells Fargo, Citigroup and US Bancorp were among the banks approached by Facebook in recent months, The Wall Street Journal reported, citing sources familiar with the matter.
The offer was part of the company's efforts to become not just a platform where people can connect with their friends, but also one for selling goods and services, the publication noted.
Banks struggle to increase their customer base, something which may push them into deals with the largest social media platforms, which accumulate billions of users, the newspaper added.
The social network said it had pledged to protect banking data from third-parties and would not use it in ad targeting.
Facebook faced sharp criticism in March after it emerged that personal data of about 50 million of its users had been harvested by Cambridge Analytica without their permission via a special app. The information was allegedly used to help target political advertising. In early April, Facebook estimated the number of users affected at around 87 million.
In late July, Facebook shares slumped more than 20 percent after its second-quarter report showed a slowdown in the company's revenue and growth of its active users database.