Senior MPs want to call former Financial Services Authority (FSA) chief executive Hector Sants before the banking standards commission to explain how he will overhaul Barclays' troubled culture.
Sants is joining Barclays as head of compliance next year but is already facing questions about his decision three years ago to clear one of the bank's most controversial deals, the Telegraph reports.
This involved moving $12.3bn (£7.5bn) of toxic assets into an off-balance sheet company called Protium.
Mark Garnier, a member of the parliamentary commission on banking standards, told the Telegraph he now wants Sants to give evidence before the sub-panel on corporate governance.
"I would like him to explain how he is going to change things at Barclays and to ask him about his judgment on Protium," Garnier said.
A spokesman for Sants said he would be "happy to provide evidence" if asked to do so.
MPs would also like to ask Sants about his decision to clear Bob Diamond to become chief executive of Barclays, despite a culture of aggressive risk-taking being allowed to develop at the bank.
Barclays chairman, Sir David Walker, is heading a comprehensive review of the bank.
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