Energy Secretary Ed Davey said he wants to bring Ofgem in line with other regulators such as Ofcom and the Financial Services Authority, who can ensure compensation goes to customers.
Currently energy suppliers voluntarily give cash to consumers following errors - but there is no obligation - while Ofgem has been able to fine companies, but that money has gone to the Government.
The redress could include pound-for-pound compensation, goodwill payments or public apologies.
More top news
The first behind-the-scenes photographs of George Clooney and Amal Alamuddin's Venice wedding have been published in a celebrity magazine.
The US Secret Service chief faces questions from politicians today over the latest in a series of worrying White House security breaches.
On average it is looking like September 2014 will be the driest for over 100 years.