The Dow Jones website All Things Digital said the shakeup of the struggling Internet giant could come as early as the end of March and could target Yahoo's public relations and marketing division, research, and region-focused and other marginal businesses.
The layoffs "are likely to number in the thousands", the website said, citing "multiple sources" inside and outside the company.
The California company had more than 14,000 employees at the end of 2011.
Yahoo! declined to comment directly on the story.
But in an emailed statement, the company said: "As we have indicated, our leadership is engaged in a process that will generate significant strategic change at Yahoo, but final decisions have not yet been made at this point."
Thompson, formerly the chief of mobile payments firm PayPal, promised urgent action to turn the company around after taking the job at the beginning of January as turmoil over the future and poor financial results engulfed the company's management.
At the same time several longstanding board members, including company co-founder Jerry Yang, resigned.