Outgoing Culture Secretary Baroness Morgan told Peston she would like to see the non-payment of the BBC licence fee decriminalised.
Speaking to Robert Peston, Baroness Morgan said the "way people consume media" is changing and that it might be more suitable to launch civil proceedings against those who did not pay the licence fee.
Baroness Morgan told Peston: "The broadcasting landscape has changed, even in the five years since the last review.
"Is it right that we criminalise people for not buying a licence fee, when we don't criminalise people for not paying other bills?
"We're not saying there shouldn't be sanctions, but you could have a civil sanction."
When pressed by Peston about what form of punishment those who don't pay the fine could face, Baroness Morgan added: "The sanction would be that you would end up going to the courts, going through a civil procedure, potentially to enforce the non-payment of a fine.
"Of course the other big change that's happened is that from May of this year, those who are over-75 not on pension credit will be paying the licence fee as well, and we actually know that of course it's often women who will find they are the ones who will fall foul of the system."
Critics argue that if the licence fee was scrapped, there would be less money for the BBC to put on television programmes and would reduce its revenue.
Speaking of that criticism, she said: "There's a broader debate to be had about the licence fee and the way young people consume news... let's have that debate."
Baroness Morgan will resign from her role as Culture Secretary on Thursday as part of a much-anticipated Cabinet reshuffle.
Under current regulations, a licence is required if you watch or record programmes shown on the BBC, or downloaded from BBC programmes on iPlayer.
The current cost is £154.50, but is set to rise to £157.50 from April this year.
Other guests on Peston include Len McCluskey, Jeremy Hunt, Rosena Allin-Khan and Baroness Warsi.