Citing unnamed sources, multiple reports said John Thornton, who shares the title of co-chairman with Munk, will be named chairman.
The company declined comment on Munk's future Monday, except to say it will provide an update later this week.
"We don't have any comment on that speculation, except to say the company will provide an update following the board meeting this week," Barrick spokesman Andy Lloyd said in a statement.
The company had promised in October that it would update investors on plans to rejuvenate the board by the end of the year with changes expected to take effect at its next annual meeting.
Barrick has faced pressure since before its annual meeting earlier this year when shareholders voted against a largely symbolic executive pay resolution.
The company was criticized for a $11.9-million signing bonus paid to Thornton that was part of a $17-million payment package he received last year.
Barrick (TSX:ABX) has since been working to strengthen its governance practices and add independent directors to its board. The gold miner currently has seven independent directors on its 13-member board.
Munk founded Barrick and has seen it grow into one of the world's largest gold miners.
But the company, which has seen its shares plunge more than 50 per cent this year so far, has faced significant challenges as it has struggled with a falling price of gold and challenges at its operations.
Barrick slashed its dividend and has taken more than US$9.3 billion in write downs or other impairment charges to its operations around the globe this year.
The company also suspended most of the work at its massive Pascua-Lama project in South America.
Thornton, a former president of U.S. investment bank Goldman Sachs, joined the board at Barrick in February 2012 and was appointed co-chairman five months later.
Though he has little direct mining experience, Thornton has strong ties to China as chairman of the advisory board at the Tsinghua University School of Economics and Management in Beijing as well as other experience.