Microsoft shares closed up 3.81 percent, to 89.81, in heavy trading.
On Friday U.S. District Court Judge Thomas Penfield Jackson named Judge Richard Posner, head of the U.S. Court of Appeals in Chicago, to oversee negotiations toward settling the landmark case. Jackson called the move "voluntary mediation" and said Posner would be "acting in a private capacity."
Some experts said the appointment of Posner, who is considered skeptical of a number of antitrust theories on which the government's case is based, increased the possibility of a settlement and lessened the likelihood that Microsoft would be dismantled as a remedy in the antitrust case.
The news lifted Microsoft's stock more than three points in after-hours trading on Friday. The company was trading at 89.69, after closing the day at 86.
In related news, a group of lawyers in California today filed a class-action lawsuit against Microsoft today on behalf of millions of citizens.
The suit could be the first of many private suits to be filed against the software maker charging that the company overcharged consumers for its Windows operating system.