The Chancellor is thought to be considering scrapping a 3p a litre rise in fuel duty due this autumn.
But motoring groups called on the Government to cut the tax on petrol.
FairFuelUK spokesman Quentin Willson said: "Scrapping the planned autumn rise may be a welcome signal that the Government is listening but, if these reports are correct, families and businesses will be devastated that fuel duty isn't going to be cut next week.
"The country wants a reduction in their petrol and diesel bills, and actually lowering duty is the only way to offer that."
However, Jason Torrance, of sustainable transport body Sustrans, said scrapping the rise would be an expensive mistake which would cost £1.5 billion. He added: "If the Prime Minister and the Chancellor really want to tackle the cost of living for Britons, they need to give people a choice about how they travel by making affordable forms of transport."
The Government said fuel would cost 10p a litre more if it was not for previous scrapped increases.
But motoring groups warned fuel costs could hit record levels again. AA president Edmund King said: "High fuel costs hit not only drivers but the entire economy."
l Downing Street is considering plans to privatise national assets instead of a further round of spending cuts, with a review being carried out by a civil servant, according to reports.
Coalition ministers are under pressure to come up with extra cuts but some departments have said they can cut no more.
But any suggestion that assets were to be privatised on a large scale would led to accusations that ministers were trying to "pawn the family silver".