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The briefing will be held at 1500 GMT, the SARB said in a statement without providing further details.
The City Press newspaper reported on Sunday that the bank is expected to be placed under curatorship this week by the SARB. Officials at VBS Mutual Bank could not immediately be reached for comment.
In 2016, the bank was thrust into the spotlight when it provided a 7.8 million rand ($660,000) loan to former president Jacob Zuma to reimburse the state for upgrades to his personal home - one of many scandals that plagued his administration.
According to its 2016 annual report, its total assets were around 1 billion rand ($85 million), and any failure would not pose a systemic risk to the wider economy.