Chief executive Oliver Morley tweeted a photo showing a "prototype" using Apple's Wallet app on an iPhone.
He says it will be an "add-on" to the plastic card rather than a replacement.
Wallet already stores boarding passes and credit, debit, gift and discount cards. Payment information is encrypted end-to-end and authorised with the user's fingerprint or passcode.
CCS Insight analyst Ben Wood said: "Security has taken a significant step forward to support digital payments on phones, so the framework is in place for other secure applications, such as a digital driving licence.
"There are not many people in the UK that do not carry a smartphone with them every day, so it is a logical next step."
Chris Green, technology analyst at the business consultancy Lewis, said digital wallets were "a massively underrated and under-exploited resource".
"People are getting more and more used to the technology because of e-ticketing," he said.
"People are far more comfortable with the concept of keeping key information on their smartphone."
DeLaRue, which prints British banknotes and passports, has already said it is working on a paperless passport.
And the NHS has announced a Â£4bn plan to move to a "paperless" platform.
Morpho Trust, a US security company that provides driver's licences, has been piloting a digital licence product in Iowa since August 2015.
It says it:
And in Australia, the New South Wales government has announced the introduction of digital licences, which it says will eliminate the need for a physical card.
The first licences issued under the new system are for fishing, the purchase of alcohol, and responsible gambling.
A driver's licence is due to be available in digital format by 2018.
The UK's Driver and Vehicle Licensing Agency is working on a smartphone version of its driving licence.