Chief Secretary to the Treasury Danny Alexander, a Liberal Democrat MP, will announce he is proposing to allocate funds for a fuel subsidy to the postcodes, all of which are in LibDem-held constituencies.
The areas named will include Strathcarron, Ullapool, Highland, Lairg, Mallaig, Hallkirk and Oban.
Also listed will be Hexham, Northumberland, a constituency held by a Tory MP.
Ministers have submitted an application to the European Commission to apply the subsidy to a total of 17 of the most rural parts in the UK.
The first 10 areas were announced last year.
They caused controversy because of the high number in LibDems' constituencies.
Under the proposals drivers could expect to see up to five pence per litre cut from the price of fuel.
The scheme is already in action in some island communities.
A final decision on how far it will be extended is due to be announced by the Commission later this year.
Mr Alexander said: "High fuel prices in areas where cars are a necessity, not a luxury, is a major issue in rural communities across the UK."
He added: "Reaching agreement with the Commission will not be easy, but we will now get on with making that case as strongly as we can."