Capital One, a Warren Buffett-backed consumer bank and credit card issuer, will acquire the credit card lender Discover Financial Services, according to a report by The Wall Street Journal that cited people familiar with the matter.

Capital One has been working with advisers to "study a deal" to buy Discover and a deal could be announced as soon as Tuesday, per the Journal's report. Bloomberg reported earlier Monday that Capital One was considering making an offer for Discover.

Discover has a market value of roughly $28 billion and the Journal reported that an acquisition would be expected to value it at a premium beyond that valuation.

In January, Discover and Capital One reported declines in fourth-quarter profits of 62% and 43%, respectively, as banks increased provisions for losses from bad loans as rising interest rates raised the risk of consumer defaults on credit card debt and mortgages.

This is a developing story. Please check back for updates.

Reuters contributed to this report.