A ban on the sale of new petrol, diesel and hybrid cars could be just 12 years away.
Transport Secretary Grant Shapps said a consultation on the plan – part of the Government's drive to tackle climate change – would include 2032 as a possible cut-off date.
Boris Johnson last week announced the Government's intention to bring in the ban by 2035 at the latest, five years earlier than had previously been proposed.
That led to protests from car manufacturers that the Government was "moving the goalposts".
Now Mr Shapps has said the end for cars and vans powered by internal combustion engines could come three years sooner.
"The Prime Minister last week has said we would like to do that by 2035 at the latest," he told BBC Radio 5 Live.
"We have said 2035 or even 2032."
The Government aims to shift drivers towards electric vehicles as part of the effort to reach net zero emissions by 2050.
Mr Shapps, who drives an electric car, said the Government was investing around £1.5 billion in infrastructure for the shift away from petrol and diesel.
He added: "We have domestic car producers and we want to help them to transition so we are doing a lot of work – in fact tomorrow I'm meeting with the car manufacturers on this very subject."
Mr Shapps said there were "now more public charging locations than petrol stations in this country" and "electric cars are coming and we want to help the country transition".