Van Saun, who hails from Pennsylvania, has been tipped to return the United States to run the bank’s Citizens subsidiary ahead of a planned flotation, which was unveiled last month.
RBS declined to comment on either appointment. Both could be announced within weeks, according to sources.
Bostock, a former Abbey National finance director, has been in his current post since 2009.
He was expected to move to Lloyds Banking Group in 2011 but withdrew because he was concerned by the health problems suffered at the time by António Horta-Osório, the Lloyds chief executive who approached him. It is thought he may have been promised a promotion if he stayed on at RBS.
Van Saun, who has held his current role since October 2009, is a key member of the team that has restructured the RBS balance sheet, mainly through asset sales. RBS hopes to complete its rundown of “non-core” assets this year as chief executive Stephen Hester approaches the end of a five-year turnaround plan.
Van Saun was previously chief financial officer at Bank of New York Mellon, where he worked from 1997 to 2008. He has also worked at Deutsche Bank, Wasserstein Perella Group and Kidder Peabody & Co.