The once mighty Citigroup (C) is mulling selling business units, or the entire company as the banking giant's market value has plummeted in recent days.

Shares of the second largest U.S. bank by assets have been under intense pressure -- falling as much as 26% in recent trading sessions -- as rumors have swirled about whether the company can weather the hurricane that has slammed the financial sector. 

Check Out Citigroup's 'Off Balance Sheet Arrangements'

According to a report by the Wall Street Journal, Citigroup's top management and board of directors are in preliminary internal discussions about the future of the bank. 

Citigroup CEO Vikram Pandit reportedly held a global conference call Friday morning, reiterating the company's strong capital position. Pandit also said Citi is not considering selling off Smith Barney -- the company's asset management business -- according to sources within the company. A company spokesperson declined to comment on the matter. 

There is also speculation among industry participants that the bank is in contact with the government regarding further capital assistance.  Neither Citi, the Fed, nor the Treasury were available to comment. 

Shares continued falling Friday -- closing 94 cents, or nearly 20%, lower to $3.77. Indeed, options activity in Citigroup was heating up as well. 

One particular type of option -- December 2.5 puts -- which is a bet that Citi shares will fall below $2.50 before expiration by the third Friday of December, reached 50,000 contracts on Friday. The heavy volume is usually an indication of institutional participation, and occurred with companies such as Bear Stearns, Lehman Brothers and American International Group as well.

Top executives, including Pandit, have made significant purchases of Citi stock recently in a vote of confidence.  The purchases have cost them dearly, though -- Pandit has lost over $4 million this week. 

As a result of the decline, Citi has pushed regulators to reinstate a ban on short selling financial stocks, according to a report by the Wall Street Journal. Short selling is when traders borrow a stock and pay for it at later point, hoping the stock price will fall. Some industry participants blame short sellers for rapidly depressing stock prices, but it is not widely agreed upon. 

The bank insisted Thursday that it "has a very strong capital and liquidity position" and it remains focused on cutting expenses and selling assets. 

Ladenburg Thalmann's Dick Bove also lent his support to the beleaguered bank. 

"I would be a buyer of this stock," he wrote in a research note Thursday. "It would take a Depression every bit as large and long as the 1930s debacle to shake this company's viability."