The Ministry of Justice is to announce the end of the ban on cameras in law courts.
Reports suggest David Cameron is preparing to announce the plans in a speech on crime, The Guardian newspaper and others claimed.
The MoJ said in a statement that was repeated by Number Ten: "We are considering proposals put forward by broadcasters to allow limited recording and transmission from courts in specific circumstances.
"However, before any firm proposals are developed, the Lord Chancellor will wish to consult on the principle of broadcasting from court with the senior judiciary."
Speaking on Sky News, Justice Secretary Ken Clarke said he could see “no good reason” why television cameras should not be allowed in court to “record and give to the public the remarks of the judge”.
"We don't want theatre," he said, adding: "cameras in court are worth trying to demystify the process... What we need is public confidence and transparency."
Sky News has been campaigning for the change for some time. On Monday it quoted its own sources who is said had confirmed cameras would be allowed into courts.
John Ryley, who is the head of Sky News, announced a campaign to televise some court proceedings in January 2010, and has written to Justice Secretary Ken Clarke to call for the move.
Speaking on Monday Ryley said: "Sky News welcomes the decision and looks forward to working with the judiciary to bring about more transparency in our justice system."
John Whittingdale MP, who is chair of the culture select committee, told Sky News: "It seems to me fairly evident that if we want to encourage people to understand the law, respect the law more and the judicial process... then this has to be the right thing to do."
Whittingdale said the details of the proposal were still to be established, but said he could not argue with the essential idea.
"I think the principle is one that I hope most people will support," he said.