E*Trade Financial's ( ETFC) writedown woes that sent the stock spiraling Monday have renewed analyst speculation about the possibility the online broker could sell itself. E*Trade shares were rebounding almost 14% on Tuesday, after dropping nearly 60% on a string of bad news Monday and late Friday, including a Citigroup downgrade and accompanying note that said the company's bank was in danger of failing and the company's warning that it expected writedowns to its $3 billion asset-backed securities portfolio. While bargain hunters were returning to the stock Tuesday, analysts were focused on repercussions for the business -- including the possibility of a sale. "We expect that the company is aggressively pursuing various alternatives to deal with the bank deterioration," Richard Repetto, an analyst at Sandler O'Neill & Partners, wrote in a note Monday. He downgraded the stock to hold from buy. "CEO Mitch Caplan will pursue what's best for shareholders and would step aside/give up control of the company if an appropriate transaction was presented," Repetto added. One possible buyer is rival TD Ameritrade ( AMTD); market chatter this spring indicated it was in discussions with E*Trade over a possible merger. TD Ameritrade has been pressured by two big activist hedge funds to merge with an industry peer -- namely E*Trade or Charles Schwab ( SCHW). Even without a sale, TD Ameritrade, Schwab and Fidelity could benefit from E*Trade's troubles by picking up retail brokerage clients. A spokeswoman for TD Ameritrade did not return requests for comment.