The energy regulator said that it might insert two new reviews a year, one in January and another in July.
It would help pass on savings from a potential fall in gas prices to customers more rapidly, Ofgem said, and also protect under-pressure energy suppliers from being damaged by the cap.
“Today’s proposed change would mean the price cap is more reflective of current market prices and any price falls would be delivered more quickly to consumers,” said Ofgem chief executive Jonathan Brearley.
“It would also help energy suppliers better predict how much energy they need to purchase for their customers, reducing the risk of further supplier failures, which ultimately pushes up costs for consumers.
“The last year has shown that we need to make changes to the price cap so that suppliers are better able to manage risks in these unprecedented market conditions.”
After a consultation, Ofgem hopes that the changes could come into force from October, meaning the first change under the new system would be made in January.
The energy price cap – currently at a record £1,971 per year for the average household – is reviewed every six months and changed in October and April.
Ofgem considers a range of information when deciding where the price cap should be set. The price that energy suppliers pay for the gas and electricity they buy is a major part of this.
Over the last year gas prices have risen so rapidly that suppliers were often forced to sell the gas for less than they bought it for due to the price cap.
By changing the price cap more often, Ofgem will make it more reflective of international gas prices, taking some of the pressure off suppliers.
The proposed changes to the cap will also allow suppliers to recover some other costs in a better timescale.
“Our top priority is to protect consumers by ensuring a fair and resilient energy market that works for everyone,” Mr Brearley said.
“Our retail reforms will ensure that consumers are paying a fair price for their energy while ensuring resilience across the sector.”