Chief Treasury Secretary Danny Alexander's constituency at Inverness, Nairn, Badenoch & Strathspey would benefit from the scheme. He put forward his views:
"As a Highlander, I know all too well that fuel prices tend to be highest in areas where a car is needed the most.
"We've already delivered a tax cut for remote islands and now want to extend that to mainland rural areas that suffer from similarly high prices to the islands.
"We have put together the strongest possible evidence base to try and maximise the places that get it. As I've said before, it won't be easy to get this agreed with the Commission, but I will do everything I can to make this happen."
Hawes in North Yorkshire is among ten areas that could benefit from a 5p-per-litre fuel duty cut.
The Government has applied to the European Commission to vary the duty rates.
Discounts have never been permitted before, but Chief Treasury Secretary Danny Alexander said the 'strongest possible evidence' had been put together to make sure an extension goes ahead.
Hawes was chosen because it has higher pump prices than other locations that already receive a discount. It is also more than 100 miles from the nearest refinery, and has a population of fewer than 135 people per square kilometre.
The commission is expected to announce its decision next year.