Microsoft has renewed talks with Yahoo with an eye to forging a business relationship that falls short of a full buyout, the company said in a statement released over the weekend.

"Microsoft is considering and has raised with Yahoo an alternative that would involve a transaction with Yahoo but not an acquisition of all of Yahoo," Microsoft said.

The company added, however, that it hasn't definitively ruled out a fresh attempt to acquire Yahoo outright. "Microsoft isn't proposing to make a new bid to acquire all of Yahoo at this time, but reserves the right to reconsider that alternative depending on future developments and discussions that may take place," Microsoft said.

Microsoft offered no further specifics on the substance of its envisioned partnership with Yahoo, but Internet speculation was rife Monday that any deal would result in Microsoft operating Yahoo's Web search business.

Driving that speculation is the thought that Yahoo and Microsoft's search units, combined, could challenge Google for a bigger share of the search advertising market. Together, Microsoft and Yahoo would control about 31% of the search market, compared with Google's 60%, according to comScore.

Microsoft's latest overture to Yahoo comes days after corporate raider Carl Icahn nominated a slate of directors to oppose Yahoo's current board at its July 3 annual meeting. Icahn's plan is to install a board that would be amenable to a merger or partnership with Microsoft.

Yahoo's current board rejected outright Microsoft's $33 per share takeover offer. Microsoft subsequently broke off acquisition talks.

Yahoo on Sunday said in a statement that it's open to a Microsoft partnership, as well as other options for boosting its search business. "Yahoo's board of directors will evaluate each of our alternatives, including any Microsoft proposal, consistent with its fiduciary duties," Yahoo said.

Yahoo shares gained .07% in Monday trading, rising to $27.68. Microsoft shares were off 1.77% to $29.46.