The search company apparently plans to say Thompson is stepping aside for personal reasons.
Thompson has been the focus of questions about a discrepancy in his IT credentials and in official documents that the company filed with the U.S. Securities and Exchange Commission.
Thompson's resume and the SEC filings say that the CEO has a college degree in computer science, but he does not have such a degree. The company called it an "inadvertent error" when questions about Thompson's background arose earlier this month, but industry analysts and critics have cast doubt on that explanation.
There was no immediate confirmation of the move from Yahoo.
In a letter Wednesday to Yahoo's board of directors, Daniel Loeb, CEO of hedge fund Third Point LLC, urged the board to move quickly to appoint an interim CEO and search for a permanent replacement for Thompson. Third Point is one of Yahoo's largest investors; Loeb has been the company's most vocal critic since the news broke that there was a discrepancy about Thompson's IT credentials.
Last Tuesday, Thompson sent a memo to Yahoo employees, apologizing for the distractions that the company is dealing with. He did not, however, make any reference to his resume.
That same day, Yahoo announced that director Patti Hart would not seek re-election to the board at the company's 2012 annual shareholder meeting. Hart led the search committee that hired Thompson, and was criticized for not fully vetting Thompson's resume.
Yahoo's board of directors also formed a special committee to investigate Thompson's academic credentials, as well as documents and circumstances surrounding his hiring earlier this year.
Jeff Kagan, an independent tech industry analyst, said Thompson is leaving "after a poorly handled controversy over a computer science degree.
"Yahoo has been struggling over recent years and this new incident only makes matters worse for the company," Kagan said in e-mailed comments about the Yahoo decision.
He said that Yahoo has "tried several strategies with several CEOs.... This CEO mess is going to leave Yahoo all tied up for at least several more quarters."