Lloyd's chairman Lord Levene of Portsoken would "not have the time" to take on the deputy chairman role at J Sainsbury full-time, according to Lloyd's sources.
According to reports, Lord Levene may step up from his non-executive director role on the supermarket's board to be the interim deputy chairman.
Sir Ian Prosser, the former chairman of the brewing and hotel mulitnational Bass, had to reject the deputy chairman's job only four days after his appointment was confirmed.
Lord Levene, described as a "safe pair of hands" would also face corporate governance issues if he were to hold both chairmanships, said sources.
