Sky News reports that they can reveal that board members at RBS are discussing the framework of a process to identify a replacement for Sir Philip, who was parachuted into the bank in early 2009 as it fought for survival.
Insiders said that Sir Philip had yet to set a firm date for his departure but suggested that next year's annual meeting was a possible exit point.
External headhunters have not yet been appointed but are likely to be in the coming months, they added.
Leaving in May next year would coincide with the date of the general election, meaning that RBS's board is likely to seek a candidate who would be acceptable to all of the main Westminster parties.
The search for a new chairman will be led on RBS's side by Sir Sandie Crombie, the former Standard Life boss who serves as the bank's senior independent director.
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