The poll by consultancy firm Accenture found 23 per cent of current account holders in Scotland would consider using a bank which does not have any street branches.
With "purely digital" banks, all interactions would be done online, making a high street presence redundant.
Royal Bank of Scotland last month warned branch closures were inevitable after a decline in face-to-face banking.
RBS has already shut around 30 banks in Scotland over the last year or so.
Chairman Sir Philip Hampton said the "continued rapid change" in the way people choose to bank would mean more closures.
The latest insight in the Accenture survey has raised further concerns over the sustainability of high-street banking and the impact of its decline on elderly and rural customers.
Peter Kirk, managing director of Accenture's financial services group, said traditional banks need a better online presence or they risk losing customers.
He said: "This year's survey underscores the growing complexity in how consumers want to interact with banks in the digital age.
"The youngest, most tech-savvy customers still value face-to-face contact as they begin their life's financial journey, whereas older customers who are further along in their work-life are more open to a digital-only relationship.
"There is also evidence that some customers are not satisfied by their banks' current digital offerings.
"This presents difficult questions for banks as they look to balance digital channels with costly branch networks and deliver relevant services."
Although the idea of a purely digital bank would mean it was "open" at all times, it would nevertheless have no call centres or face-to-face advisers.
Banking advice and possible services would be determined through the data provided by the user.
The same survey found that three-quarters of all mobile phone-based banking occurred on a daily or weekly basis.
However, the Accenture survey also found that customers had been visiting branches more and more over the last few years.
In 2014, a total of 48 per cent Scots visited their banks on either a daily, weekly or monthly basis, compared to 42 and 41 per cent for 2011 and 2012, respectively.
Complaints and dispute resolution may also be a problem as the majority of respondents say they would be reluctant to communicate with their bank through virtual channels.
Only 19 per cent said they would like to contact their bank through an instant messenger service. 15 per cent said they would do so through video chat, while just nine per cent thought social media banking was preferable.
Mr Kirk added: "To grow their business and increase market share, banks need to differentiate themselves because customers feel that most banking products and services are more or less the same, and there's not much point in switching.
"This is becoming increasingly important in the digital world as customers are in the driving seat, and they expect the same level of convenience, simplicity and speed from banks to that which they have become accustomed to from many other service providers they use every day.
"As banks develop their strategies for re-engaging with their customers, they will need to focus on evolving customer behaviours and digital experience, while improving their services through the use of analytics and customer loyalty."