Black, 69, informed the executive committee of MoMA's board of his intention at a specially convened remote meeting on Friday, the report said. (bit.ly/3tRxSRY)
MoMA did not immediately respond to a Reuters request for comment.
Earlier this week, Black stepped down as chairman of Apollo, which he co-founded 31 years ago, months after relinquishing his position as chief executive officer of the company in January following a report by law firm Dechert.
An independent review by Dechert revealed that Black had paid late financier and convicted sex offender Jeffrey Epstein $158 million for advice on tax and estate planning and related services between 2012 and 2017.
Although the review cleared Black of any wrongdoing, a series of corporate governance changes triggered by the review forced Black to step down from his executive positions at Apollo. Reporting by Sohini Podder in Bengaluru; Editing by Shinjini Ganguli