Nathan Bostock, who was appointed as group finance director at RBS on October 1, is understood to be in talks to join the Spanish bank Santander as its chief risk officer.
He informed the board tonight of his intention to tender his resignation.
In a statement, the bank said: "The Royal Bank of Scotland Group can confirm that Nathan Bostock has this evening informed the Board of his intention to resign from his role as Group Finance Director.
"His formal resignation is expected soon, but he will remain in his position to oversee an orderly handover of his responsibilities.
"Details on arrangements for his successor will be announced in due course."
Mr Bostock's appointment as group finance director at RBS followed four years as head of restructuring and risk at the bank.
Before joining RBS, he spent eight years with Abbey National in several roles including chief financial officer and as a main board director responsible for products and marketing, HR and insurance and cards.
He had previously spent 10 years with RBS in a number of roles, including chief operating officer of treasury and capital markets and group risk director.
Mr Bostock almost left RBS to join Lloyds Banking Group in 2011 but the plan was abandoned after Lloyds boss Antonio Horta-Osorio took three months' sick leave, due to exhaustion.
The news of his departure from RBS comes after a week after IT problems left some customers unable to use their debit or credit cards or access their accounts.
RBS chief executive Ross McEwan admitted that it had failed to invest properly in systems for decades after a computer glitch left customers of RBS and its NatWest subsidiary unable to use credit and debit cards for three hours on the busiest online shopping day of the year.
Days later RBS said its websites were the victim of a cyber attack that caused the group's sites to go down and left some customers unable to access their accounts.