The watchdog is investigating payments between the bank and Qatar’s sovereign wealth fund.
The paper said it had learned Varley is one of four current or former executives that the FSA is investigating over “advisory fees” paid by the bank to Qatar Holding in 2008.
The report said payments were linked to the sovereign wealth fund’s participation in an £11bn bailout that saved Barclays from collapse during the credit crisis.
Last week the bank confirmed it was being investigated by the Serious Fraud Office (SFO) in relation to the payments.
The Sunday Telegraph said the investigation into Varley would hurt his chanced of becoming the next governor of the Bank of England. It added if he was found to have breached regulatory rules he could be banned from working in financial services entirely.
Chris Lucas, incumbent finance director, and former head of investment banking from the Middle East, Roger Jenkins, are known to be two of the four executives under scrutiny.
Varley ran the bank for six years, prior to Bob Diamond who took over in 2010.
