The proposal to cut 5p off a litre in the locations north of the Border, along with three areas in England, would save drivers £3 every time they fill up their tanks.
The UK Government has confirmed it has made its bid to the European Commission to replicate in certain mainland rural areas the already successful rebate scheme introduced for some islands.
If Brussels agrees, Britain will become the first EU member state to have an inland fuel rebate scheme; other countries such as France and Portugal currently, like the UK, have island rebate schemes.
The Coalition asked for pump price data from a range of council areas, including Argyll and Bute, Dumfries and Galloway and the Highlands.
It has now completed its assessment of all the evidence and concluded seven areas in Scotland and three in England meet the strict criteria.
The Scottish areas the Government wants to benefit are Acharacle, Achnasheen, Appin, Carrbridge, Dalwhinnie, Gairloch, and Strathpeffer. The English areas are in Cumbria, Devon, and North Yorkshire.
The criteria are:
l Pump price threshold - prices have to be consistently more expensive than the lowest on the islands in the existing scheme, during the months examined;
l Transportation costs - towns have to be more than 100 miles by road from the nearest refinery;
l Population density - this must be no higher than any area in the current scheme; the highest population density of the islands in the current scheme is 135 people per square km.
If the extension is approved - a decision is expected next year - then it would raise the number of people in the UK benefiting from the rural fuel scheme to nearly 120,000.
Announcing the EU bid, Danny Alexander, Chief Secretary to the Treasury and MP for Inverness, Nairn, Badenoch and Strathspey, said: "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 have 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 have 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."
The Treasury accepts the "bar is high", not least because if the UK gets a mainland scheme, other member states will be queuing up to get the same fuel discount.
The current rural fuel scheme came into effect in March last year. It allows garages within the Inner and Outer Hebrides, the Northern Isles, the Islands of the Clyde and the Isles of Scilly to claim back from HM Revenue and Customs 5p per litre on unleaded petrol and diesel for retail sale within the eligible areas.
Labour's Catherine McKinnell said she hoped the Government's move would mean some relief for rural drivers but pointed out eight of the 10 areas mentioned had Liberal Democrat MPs, including two in Mr Alexander's constituency.
"The public will want to be reassured this is no more than a coincidence because no-one will thank a LibDem Treasury Minister who refuses to tackle the cost of living crisis everywhere but his own back yard."
The AA said this week motorists are enjoying the biggest fall in petrol prices since the credit crunch days of 2008, with a litre now costing an average of 132.16p. But the organisation warned a further dip in prices is unlikely.