Reports indicate that Yahoo is considering unloading its search business, and focusing on its stronger media business.

Last month, we reported on rumors that Yahoo’s “Search Alliance” with Microsoft may not play out for its full ten years.

Motivity Marketing CEO Kevin Ryan said, at the time, “There’s a lot of rumors in the business that [it] isn’t going well, and that it’s not going to make the full-decade run.”

Now, Kara Swisher at All Things D reports, “Yahoo is also considering turning its entire search business over to Microsoft, with which it already has an ad partnership.”

Eric Jackson at Forbes has some interesting ideas for options for Yahoo, which, also include exploring partnerships with Facebook, Apple, or even Google. Given the the company’s relationship with Microsoft, the concept Swisher is reporting on seems like it makes the most sense, though there’s always the possibility that the two companies could rework their current deal, as Jackson notes.

Yahoo launched its most significant contribution to search in recent memory when it launched Axis, its browser add-on/mobile browser, last month. As an add-on, it was clunky and intrusive, but as a mobile browser, it had some advantages over Safari, giving iPhone and iPad users a legitimate browser alternative.

Yahoo launched Axis for iOS first, seemingly trying to combat Google in a place where it wasn’t dominant – as a browser on Apple’s popular devices. Unfortunately for Yahoo, Apple announced significant upgrades for its own Safari browser at its Worldwide Developers Conference last week, including Chrome-like search functionality, which will give people already used to Safari less reason to switch over to Axis.

Of course none of this means that Yahoo will completely abandon search. You might say Axis was a sign that the company is still very much interested in search. Then there’s the fact that Yahoo’s search market share stopped spiraling downward, according to the latest comScore numbers.

Still, media seems to be Yahoo’s strong suit. Just last week, Yahoo announced a major partnership with CNBC to share revenues and news content.

Yahoo’s homepage is still a major Internet destination, largely powered by the company’s media content.

While Yahoo’s leadership is still up in the air, the company did just appoint a new EVP and Chief Revenue Officer to oversee its ad revenue and global operations. That would be Michael Barrett, formerly of Google.