The leadership crisis at Barclays shows no signs of easing after the frontrunner for the role of chairman reportedly withdrew from the race.
Deputy chairman Sir Michael Rake had been tipped to replace Marcus Agius, who remains in the post only until his replacement is found.
Several top shareholders backed Sir Michael, who is also chairman of BT and easyJet, but the Sunday Times said he had told Sir John Sutherland, the non-executive director leading the search, he did not want to be considered.
With other investors indicating they want an external appointment, Glen Moreno, the former banker who chairs publisher Pearson, and Lord O'Donnell, the former Cabinet secretary, are among other names in the frame.
The bank, which was hit with £290 million of fines following the Libor affair, is also without a chief executive after the departures of Bob Diamond and chief operating officer Jerry del Missier in the wake of the scandal.
Rich Ricci, head of Barclays' investment bank, is also thought to have ruled himself out of the running to replace Mr Diamond. Naguib Kheraj, the former chief financial officer who is now a senior adviser to the bank, is seen as the one viable internal candidate.
In his temporary role as executive chairman, Mr Agius will present the group's half-year results on Friday, when profits are set to rise by 10% to £4 billion.
The higher figure, which will be driven by a stronger performance from its investment banking arm Barclays Capital, could ease concerns held by credit ratings agencies Moody's and Standard & Poor's, which both placed Barclays on negative outlook.
The newspaper added that the bank is expected to appoint Antony Salz, a veteran City lawyer, to lead an investigation into the Libor affair.