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.
Government plans to reduce fuel prices in rural areas have taken a step forward.
Fuel retailers in remote areas are being asked to let the government know how much they charge for petrol and diesel. The government is preparing to ask the European Commission for permission to extend the existing Island Fuel Rebate Scheme to remote rural areas on the mainland.
Citizens Advice in the North East is urging families and households to save money on their fuel bills during Big Energy Saving Week. People here spend less on food to pay for their other bills than anywhere else in the country. **
The service is hoping people will consider what they can do to help themselves and is using this week to call on them to consider switching energy suppliers and to look at ways to insulate their homes**
Campaigners are putting pressure on the Government to cut duty on fuel. The Tax Payer's Alliance and the Petrol Retailer's Association are setting up stands on independent forecourts to ask motorists to lobby local MP's.
Sixty pence in every pound spent on petrol or diesel in the UK goes to the treasury. UK has the highest tax on unleaded petrol in the EU.
Forecourt owners like Allan Glendinning in Prudhoe, in Northumberland, say the situation is desperate.
Campaigners against high fuel tax will be on forecourts across the region this morning to tell customers how much their petrol costs and how much money is going to the Treasury. Over 5,000 stands will be set up across the country.