John Varley, another ex-chief executive, was also named by the Financial Times as due for interview.
The interviews are part of an inquiry by the SFO into allegations about £322m ($543m) in payments during the Qatar deal.
According to the Police and Criminal Evidence Act, an interview under caution does not compel someone to answer questions. However, "it may harm your defence if you do not mention when questioned something which you later rely on in court."
The SFO has been investigating claims that Barclays paid £322m in fees to investors in order to gain their support for a £5bn ($8.43m) fundraising.
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