Antony Jenkins commented on the referendum during an interview with the BBC.
He said: "That's a matter for the Scottish people to decide - we think we can make it work either way as a bank."
Mr Jenkins' comment follows an intervention in the debate by oil giant BP's chief executive Bob Dudley, who said last week that there are ''quite big uncertainties'' surrounding independence.
Mr Dudley said: ''I'm not concerned but there's enough uncertainty and talk about it and questions raised.
''It would create extra costs for our business. We have to duplicate the centres and do things, and again the currency question I don't know the answer to.''
Stewart Hosie, SNP Treasury spokesman, said: "This is a common sense approach from Barclays Bank.
"Of course they will have technical questions that they will want answered but they are right - this is a decision for the Scottish people and I very much welcome the chief executive's comments.''