Marcus Agius is going to resign on Monday as Barclays group chairman following the row over fixing of the interbank lending rate, Sky sources say.
The bank's chief executive Bob Diamond is due to be questioned by MPs about the affair on Wednesday.
Sir Mike Rake, the heavyweight chair of BT, is believed to be the most likely candidate to replace Mr Agius.
Barclays Bank was fined a record £290m by regulators in the United States and Britain last week.
The lender agreed to pay the penalty in return for settling claims involving the manipulation of the London interbank lending rate, known as Libor, and its equivalent in Europe - Euribor - before and during the financial crisis.
Mr Diamond apologised for the bank's actions and waived his bonus.
The latest development comes as the head of the government's financial regulator calls for tighter laws to deal with failing bankers.