The proposal to ban the sale of all petrol and diesel-engined cars - including hybrids and plug-in hybrids - by 2035 could be brought forward by a further three years, according to transport secretary Grant Shapps.
Speaking as a guest on BBC Radio 5 live, Shapps said the ban would happen by 2035 "or even 2032", before stating there would be consultation before any decision is made.
The accelerated plan to bring the ban from 2040 to 2035, proposed last week has already been branded "extremely concerning" by the Society of Motor Manufacturers and Traders (SMMT).
The move, which is five years earlier than previous plans, was announced by prime minister Boris Johnson at the launch of the COP26 climate summit as part of measures to help the UK achieve net zero carbon emissions by 2050.
However, SMMT boss Mike Hawes claims the government has "seemingly moved the goalposts" without a clear plan in place to achieve the goal.
"Manufacturers are fully invested in a zero-emissions future, with some 60 plug-in models now on the market and 34 more coming in 2020," Hawes said.
"However, with current demand for this still expensive technology still just a fraction of sales, it’s clear that accelerating an already very challenging ambition will take more than industry investment.
"This is about market transformation, yet we still don’t have clarity on the future of the plug-in car grant - the most significant driver of EV uptake - which ends in just 60 days’ time, while the UK’s charging network is still woefully inadequate.
“If the UK is to lead the global zero emissions agenda, we need a competitive marketplace and a competitive business environment to encourage manufacturers to sell and build here. A date without a plan will merely destroy value today.