A majority of the settlement is expected to be in cash, but the figure also includes several billion dollars in help to struggling borrowers, the source said.
An announcement of the settlement between the bank and the U.S. Department of Justice could come as early as next week, the source said.
A Citigroup representative declined comment. A Justice Department spokeswoman did not respond to requests for comment.
A settlement of around $7 billion for Citigroup would be higher than analysts had expected based on the bank's mortgage securities business.
Some Wall Street analysts had previously estimated that Citigroup likely had about $3 billion of reserves set aside for a related settlement. U.S. authorities had demanded more than $10 billion last month, Reuters reported.
Talks between U.S. authorities and Citigroup stalled last month after both sides stood far apart on a settlement figure and the Justice Department had prepared to sue the bank.
The bank is scheduled to report second-quarter results on Monday. Analysts, on average, have estimated the company would earn $3.4 billion.
U.S. Attorneys offices in Brooklyn and Colorado have been investigating the bank as part of a larger task force probing faulty mortgage securities that helped fuel the housing bubble in the mid-2000s and contributed to its collapse.
JPMorgan Chase & Co paid $13 billion in November to resolve a range of probes from the task force, in a deal that U.S. authorities said would serve as a template for other banks. Bank of America Corp has also been in negotiations to resolve similar investigations.
(Reporting by Aruna Viswanatha in Washington and Karen Freifeld in New York, with additional reporting by David Henry in New York; Editing by Lisa Shumaker)
By Karen Freifeld and Aruna Viswanatha