The Telegraph said Stephen Hester’s replacement could come from a shortlist of about three or four internal and external candidates.
However, one source told the paper the appointment could be delayed until September due to the need for Treasury approval.
Leading internal successors are Ross McEwan, head of RBS’s retail banking unit, and Bruce van Saun, the bank’s finance director.
David Roberts, an ex-senior banker at Barclays and current deputy chairman of LLoyds Banking Group is an outside prospect.
However, ex-HSBC Hong Kong chief executive Mark McCombe – who was also in the running – has ruled himself out.
Now head of fund manager BlackRock’s Asia Pacific operations, McCombe said he rejected the offer and will remain with the world’s largest fund group.
BlackRock spokesman Brian Beades told news agency Reuters that McCombe sent a note to his senior staff informing them that he had been contacted by RBS but would stay with BlackRock.
It is thought the announcement could coincide with RBS’s financial results for the first half of the year, set for release on 2 August.