According to Swiss newspaper Tages Anzeiger, the board will make two key decisions: "first the strategy of the company, and secondly the person himself Gruebel."
Gruebel is seeking a confidence vote from the board to decide if he should stay on until early 2013 to lead the restructuring of the bank, said the newspaper.
UBS was not immediately available for comment.
UBS announced on September 15th that a rogue trader had lost the bank $2.0 billion in unauthorised trades, sparking questions about the adequacy of the firms internal controls as well as its strategy to maintain the investment bank.
That loss estimate was later revised upwards to $2.3 billion.
Pressure has mounted on Gruebel over the incident, with politicians in Switzerland calling for his resignation.
Gruebel has however told a Sunday newspaper that he was not planning to resign over the fraud, although he acknowledged that any executive changes is a decision of the board.