Its largest shareholder has spoken, and E*TRADE (Nasdaq: ETFC) is listening.

Just a couple of days after Citadel -- the hedge fund with a nearly 10% stake in the discount broker -- urged E*TRADE to seek out a suitor, the company is starting to explore its strategic alternatives.

Hiring Morgan Stanley (NYSE: MS) on Friday doesn't mean that a deal is imminent. E*TRADE hired an investment banker last year, but the broker's board ultimately decided that remaining independent would best increase shareholder value.

The decision should turn out differently this time. Trading activity has dried up in recent months, fueling sector consolidation as the easiest route to cost-cutting growth. E*TRADE's shares have also lost ground year-to-date, and that's even after last week's 21% surge on takeover speculation.

Who will buy E*TRADE, though? Let's go over the more popular candidates.

If you had to handicap the race, TD AMERITRADE would be the odds-on favorite. In fact, The Wall Street Journal is reporting that TD AMERITRADE's board will be meeting Tuesday to discuss making a run at the rival discounter.

This wouldn't be a merger of equals. TD AMERITRADE is substantially bigger, with roughly triple the market cap and more than double the trading volume of E*TRADE. However, adding a smaller rival would be the perfect tonic to help TD AMERITRADE get over the recent industrywide slump in trading activity. Investors would applaud a deal -- at a reasonable premium -- if it translates into a margin-widening bottom line for the combined company.

Charles Schwab (NYSE: SCHW)
The discounting pioneer would be the second-most-likely suitor, if it weren't still busy closing on the acquisition of optionsXpress (Nasdaq: OXPS).

Schwab may still entertain the chance to kick the tires here, if only to make sure that TD AMERITRADE doesn't get bigger on the cheap. However, it remains a long shot.

Bank of America (NYSE: BAC)
Bank of America's Merrill Lynch made a late splash in discounting with last year's launch of Merrill Edge.

Merrill Edge has been aggressive, offering $100 for new accounts and teaming up with Bank of America to offer free trades to some banking clients. If the endgame here for Merrill Lynch is to ultimately upgrade discounters into clients for its flagship full-service unit, why wouldn't it want to catch E*TRADE in a net?

Citigroup (NYSE: C)
E*TRADE CEO Steven Freiberg began working for Citigroup in 1980, fresh out of college. He rose through the ranks to head up the company's credit card and consumer banking businesses, ultimately leaving in 2009. Freiberg joined E*TRADE a year later.

Citi doesn't owe Freiberg an exit strategy at E*TRADE after three decades of service. However, Citigroup clearly knows him better than anyone else, and there has to be some interest in approaching E*TRADE for its brokerage business, now that it's making strides in cleaning up its online banking segment.

If Morgan Stanley advises a sale, and the company agrees, what happens if the only offer on the table is a lowballing TD AMERITRADE? It won't be. A handful of private equity firms might well be interested in taking E*TRADE private.

However, one can also argue that E*TRADE's own top brass may consider taking the company private, possibly with financial assistance from the private equity realm.

The next few weeks will be telling. If speculators continue to bid the shares higher, naturally it will scare away potential buyers. Brokers and private equity firms know better than to chase a deal that they don't realistically need.

The stock will then predictably fall, and we'll start this game all over again in a few months. Let's hope that if there is a win-win scenario for buyer and seller, it materializes this time. This dance is getting old.

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This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.