Citigroup has refused to comment on the reports
Shares in Citigroup closed up nearly 10% having earlier been up 17%, after reports the US government may take a bigger stake in the bank.
Taxpayers could be on the verge of owning as much as 40% of the lender's common stock, the Wall Street Journal (WSJ) reported.
The bank made an $8.29bn (£5.6bn) loss in the final three months of 2008 and was forced to split into two new firms.
The government has said it preferred banks to remain in private hands.
A joint statement from the Treasury, the Federal Reserve and other regulators concluded: "The strong presumption of the Capital Assistance Programme is that banks should remain in private hands."
The statement also reiterated that, "the US government stands firmly behind the banking system" and added that regulators would ensure banks have capital and the liquidity to provide the credit needed to restore economic growth.
The Capital Assistance Programme is the scheme that allows banks to borrow money from the government if they need more capital.
Citigroup has declined to comment on any potential plans.
"We continue to focus and make progress on reducing the assets on our balance sheet, reducing expenses and streamlining our business for future profitable growth," it said in a statement.
Last week, Citigroup's share price fell below $2 to an 18-year low.
In November, the US Treasury announced a $45bn rescue plan for the bank, accompanied by a $306bn guarantee for Citi's most risky loans, as part of its Troubled Asset Relief Program (TARP).
The WSJ said Citi was now discussing with US officials a scenario whereby a large part of that $45bn, which is currently held in preferred shares by the government, would be converted into common shares.
At present the preferred shares represent a 7.8% holding in the company.
If the move goes ahead other Citi shareholders would see their stakes diluted and the government would have a much larger influence over the bank.
The Obama administration has not indicated whether it supports such a plan.
David Trone, an analyst at Fox-Pitt Kelton warned that a greater government stake could could prompt potential customers and employees to avoid Citi.
"If we're right, the government will have a hard time ever selling its stake back to the public markets," he said.
"Nationalisation is a trap that the US government should avoid," he wrote. "If Citi is nationalised, all bank stocks are likely to get crushed in fear."
Citigroup, which two years ago was worth $273bn and is now worth just £20bn, was brought to its knees by five quarterly losses in a row.
It has been battered by the meltdown in sub-prime mortgages - made to people on low incomes or poor credit ratings.
A cost-cutting exercise last year resulted in some 52,000 jobs being slashed, bringing the Citi workforce down to about 323,000 people.