Sky News announced last night that it wants to launch a live debate on TV between the main party leaders in the run-up to the general election next year.
The news provider "hand delivered" letters to Cameron, as well as prime minister Gordon Brown and Liberal Democrats leader Nick Clegg asking them to participate.
Televised debates are already a common fixture in US presidential campaigns and are also utilised in Germany, Canada, Australia and other nations.
Writing in The Times, Ryley expressed his hope that a fair debate between leaders would help to stimulate the political process in the UK.
He also confirmed that the coverage would not be exclusive to Sky News but would be made available to other broadcasters.
"We will offer the debate live and unedited to any of our competitors that want to run it," he said.
"We are ready to sit down with them to discuss the timing and staging: this debate must be about empowering the British people; egos and self-interest must be set aside by all of us."
In an article published last month in The Independent, Clegg demonstrated his backing for a televised debate between leaders ahead of the general election.
However, Labour leader Brown is believed to favour the existing debate system in place for Prime Minister's Questions in the House of Commons.
Cameron has already said that he is up for a live debate "any time, any place", but has now moved to send Ryley a formal letter showing his backing for the idea.
In the correspondence, the Tory leader said that Prime Minister's Questions is "no substitute for a proper primetime studio debate".
"At the next General Election, people are going to face a huge choice about the future of our country," he said.
"They want politicians to be clear about where they stand. A full-length television debate has a big part to play in providing this and I look forward to working with [Sky News] to make it happen."