The source, who declined to be identified, said the board meeting was expected to address aspects of an internal review, including which board members would participate.
Mr Thompson issued an apology for the fallout from disclosures about his academic credentials in an emailed memo to Yahoo employees on Monday.
The memo came hours after Mr Loeb, chief executive of hedge fund Third Point, which holds 5.8 per cent of Yahoo’s shares, formally demanded in a letter that the internet company turn over all records related to Mr Thompson’s hiring.
“I want you to know how deeply I regret how this issue has affected the company and all of you,” Mr Thompson wrote in his first extended memo to employees since the disclosures emerged on May 3.
“We have all been working very hard to move the company forward and this has had the opposite effect. For that, I take full responsibility, and I want to apologise to you.”
He added he would “respect” the board’s plans to conduct a thorough and independent review.
Third Point, which last week revealed the discrepancies in Mr Thompson’s education record, wants Yahoo to publicly reveal the process by which he was vetted and disclose all minutes of any board meeting in which his candidacy was discussed.