The bank also revealed it is one of the banks being investigated by regulators over possible manipulation of foreign exchange markets. Meanwhile, it emerged that RBS, which has also been caught up in the probes, is reviewing how it trades in the minutes before key foreign exchange benchmarks are set.
Mr Jenkins said that customers are increasingly using online services rather than branches to manage their affairs.
"The behavioural shift is not a future change. It is happening now," he said.
"The implications of this shift are that the traditional branch model and points of contact will become less important to customers as part of the service mix over time."
He said that this will boost the savings from an ongoing restructuring programme.
Asked what proportion of branches would be cut, Mr Jenkins said: "I think that really is the wrong way of thinking about it."
He added: "There is going to be less activity in the branches.
"That doesn't mean there will not be branches.
"But it does mean that the work that happens in branches will be what matters to customers: advice on savings, on mortgages and that there will be a gradual repositioning of the network over time."
Royal Bank of Scotland has previously revealed plans to cut 10% of its network.
Mr Jenkins also wants to automate more of Barclays' administrative procedures.
"We are working on ways to automate systems that have been operating manually, reducing human error and simultaneously driving down costs," he said. He declined to specify how many jobs are likely to be lost.
"While headcount will come down over time, the vast majority of that will be achieved through attrition," he said.
The London-based bank has 22 branches and five corporate banking offices in Scotland as well as a major back office unit in Glasgow employing around 2200 people.
In February, after succeeding Bob Diamond at the top of the bank, Mr Jenkins set out restructuring plans that were expected to lead to 3700 roles going globally, although there have been reports that he anticipates 40,000 jobs being cut.
However, in Scotland, the bank recently announced it would like to increase staff numbers in Glasgow.
Barclays said of the foreign exchange investigation by regulators: "The investigations appear to involve multiple market participants in various countries.
"Barclays Bank has received enquiries from certain of these authorities related to their particular investigations, is reviewing its foreign exchange trading covering a several year period through August 2013 and is cooperating with the relevant authorities in their investigations."
"From time to time these legacy issues will arise and will have to be dealt with," Mr Jenkins said. "We are in the process of changing the culture of Barclays. I've said it will take five to 10 years to deeply embed that cultural change."
Meanwhile RBS, which has already confirmed it is working with regulators, has embarked on a review of its foreign exchange trading policies, according to emails sent to clients.
Barclays reported an underlying pretax profit of £1.4 billion for the three months to the end of September, down from £1.9bn but still better than the £1.3bn of earnings expected by the City.
Its Transform restructuring programme cost it £101m in the quarter, taking the bill to £741m so far. It was also hit by falling earnings from its investment bank.
David Hillman, spokesman for the Robin Hood Tax campaign, said: "People will rightly be angry that it's groundhog day in the City today with Barclays announcing big profits and yet more investigations into dodgy dealings."
The results are the first since Barclays completed a £5.8bn rights issue to meet new requirements set out by regulators.
Barclays' shares closed up 2.4p or 0.9% at 268.45p.