Transport minister Andrew Jones says the move would help make roads in Britain safer.
The lessons will not be mandatory and driving instructors will decide when their students are ready.
The Department for Transport is also looking at trialling a “target number” of hours of lessons to complete before learners take their test.
The proposal is one of a number of ideas being considered by ministers as part of a £2m research programme by the DfT into improving safety for new drivers.
The government said the change would allow learner drivers to “get a broader driving experience”, practise at higher speeds and put their theoretical knowledge into practice.
Mr Jones said: “We have some of the safest roads in the world and we want to make them even safer.
“These changes will equip learners with a wider range of experience and greater skill set which will improve safety levels on our roads.
For car drivers, the changes would mean that competent learners would be able to have lessons on motorways with an approved driving instructor in a dual controlled vehicle.
For those on motorcycles, the Compulsory Basic Training course – which allows them to ride unaccompanied on roads – would also be updated.
Motorcycle training would also require more online courses, with novice riders having to take a theory test.
The plans have the backing of RAC director Steve Gooding.
“The casualty statistics tell us that motorways are our safest roads, but they can feel anything but safe to a newly qualified driver heading down the slip road for the first time to join a fast-moving, often heavy, flow of traffic,” he said.
“Many are so intimidated by the motorway environment that they choose instead to use statistically more dangerous roads, so we welcome this move which will help new drivers get the training they need to use motorways safely.”
New driver Cesca Astley, who passed her test earlier this year, told BBC Radio 5 live the first time she drove on the motorway was “really daunting”.
But Ms Astley does not think these new proposals would have helped.
“I felt like passing my driving test was the confirmation I could do this. I don’t think I would have been confident [driving on the motorway] before I passed my test.”
Tim Shallcross, from road safety charity IAM RoadSmart, argues that with a little “tuition” and “supervision” learners will find the confidence to use the roads properly.
He told BBC Radio 4’s Today programme: “They’re our most inexperienced drivers, therefore we should put them on the safest roads we have.”
But Mr Shallcross said he didn’t want to see “cost obstacles” put in the way of learners and that “logged experience” could be used over “mandatory” training hours.
The Times reported on Friday that the government was also considering plans to introduce a mandatory minimum learning period for learner drivers, which could see them being made to spend up to 120 hours behind the wheel before taking their test.
A spokesman for the DfT said it was looking into a range of measures to improve safety for new drivers, including a trial of targets for the number of hours spent learning, but there were no current plans to introduce a minimum figure.
The department is also still asking for feedback from the public on the current training and testing for driving instructors.