The odds of Microsoft Corp. winning its $42.1 billion bid for Yahoo Inc. appear to be improving, but Yahoo hasn't abandoned hope of finding a way to keep the software giant at bay.

Its best chance may be a deal under discussion with News Corp., in which the media conglomerate would swap its ownership of MySpace and several other online properties for a stake of 20% or more in Yahoo, according to people familiar with the discussions. Yahoo has also reached out to others, including Time Warner Inc.'s AOL, although that option...