Shares of the company closed up nearly 12 percent at $23.55 on Friday.
The Ardsley, New York-based company, which has a market value of about $980 million, may not move forward with any formal action as the proceedings were at an early stage, the WSJ report said.
Acorda was not immediately available for comment.
The U.S. drugmaker’s investors in August had called for the company to explore a sale, after a judge in March struck down key patents of its MS drug Ampyra, which accounts for most of its revenue.
The company also recently discontinued the development of its Parkinson’s drug after reports of death.