Ross McEwan said he has not spoken to UK Business Secretary Vince Cable about moving the bank's head office, after Mr Cable speculated that it would "inevitably become a London bank" in the event of independence.
He made his comments in an online question and answer forum for The Guardian website, in which one user asked: "Vince Cable said last week that RBS would remove its headquarters from Scotland if there was a yes vote in the independence referendum. Is this the case?"
Mr McEwan replied: "We've been in Scotland for nearly 300 years. So I need to take this independence issue very seriously.
"We've also been operating in the rest of the UK for nearly hundreds of years and have a royal charter.
"It's really important that the Scottish people get the opportunity to vote, and then if I need to adapt my business to serve England, Scotland, Wales and both the Republic of Ireland and Northern Ireland, then I will.
"Mr Cable and I have not talked about moving our head office."
Barclays chief executive Antony Jenkins has already said the bank "can make it work either way" with regards to Scottish independence.
Mr Jenkins made his comments during an interview with the BBC when he said the future of Scotland was a "matter for the Scottish people to decide: we think we can make it work either way as a bank".
It follows comments by BP's chief executive Bob Dudley, who said last week there were "quite big uncertainties" surrounding independence in the run up to the referendum on September 18. He added: "I'm not concerned but there's enough uncertainty and talk about it and questions raised."
He also said he didn't "know the answer" to the currency question.