Some of the company’s biggest investors complained after news last week that Daniels, who stepped down from Lloyds last month, could succeed Lord Sharman when he leaves in 2013.
Daniels has been criticised for his role in Lloyds’ disastrous takeover of the debt-laden HBOS. The government now has a 41 per cent stake in Lloyds Banking Group.
Other names who have reportedly been considered for the role include former Labour ministers Lord Davies of Abersoch and Lord Myners.
Aviva, the UK’s biggest insurer, is now believed to have narrowed its shortlist to three candidates, with a formal decision expected in a couple of weeks.