The market’s four-day rally, where it has recouped 14% of its losses – the biggest pickup in decades – is about to get a legitimate curveball this week with a new report out from the UK-based Telegraph that Microsoft is in serious discussions to buy Yahoo. The proposed $20 billion deal isn’t for the entire company – just Yahoo’s online search business.

The Telegraph says that the removal of CEO Jerry Yang and the negotiations to buy Yahoo’s search operation were orchestrated together. The crux of the new deal is that Microsoft gets the last say over the new management team. Rumors have it that ex-AOL chairman Jonathan Miller and Fox Interactive Media Ross Levinsohn will lead the new management team.

Rumors also persist that corporate raider Carl Icahn may be pulling the strings on a Microsoft-Yahoo deal. Icahn owns over 5.5% of all Yahoo stock – a stake that Wall Street analysts peg at $850 million. Icahn was a vocal advocate of Yahoo accepting the original $47 billion deal that Yahoo, led by a reluctant Jerry Yang, turned down. Now, with Yang out of the way, the coast is clear for another shot at Microsoft, which should boost Yahoo’s stock price and give the company some much-needed capital – about $2 billion annually, Wall Street already estimates.

Already Microsoft has promised Yahoo a new $5 billion facility for its new search company, with investors supplying an additional $5 billion to get the new Yahoo-Microsoft operation up and running, and also buy stock shares in the new company. For their efforts, new investors would get first crack at preferred stock shares and warrants, and also get to appoint three new director to the Yahoo board.

Yahoo would maintain some independence with the deal. Says the Telegraph, “the talks with Yahoo involve Microsoft obtaining a 10-year operating agreement to manage the search business. It would also receive a two-year call option to buy the search business for $20 billion. That would leave Yahoo to run its own e-mail, messaging, and content services.”

The move is a clear attempt by Microsoft to gain some ground on Google in the online advertising marketplace. Right now, forecasters say that the overall market is worth $40 billion, with Google owning 77% of market share, compared to 18% and 5% for Yahoo and Microsoft, respectively.

It’s an interesting concept. All along, Microsoft chief executive officer Steve Ballmer says that he is not interested in buying Yahoo, lock, stock and barrel. But he does like the search engine possibilities of a Yahoo/Microsoft alliance and now will get a chance to find out how far that will fly.

Short-term, look for a stock pick-up for Yahoo, which has been mired in the $11 trading range. Microsoft should pick up steam, too, but maybe with a lag effect as investors mull over the wisdom of taking Google on using Yahoo as bait.

In the end, we’ll find out if a big technology giant can just wade in and buy market share in the online search world. If Microsoft can hang on to Yahoo customers, and that’s a big if, considering the history between the two companies, then Ballmer will have won his bet.

If not, then there is really nobody else left for Microsoft to buy . . .