David Cameron, Nick Clegg and Ed Miliband will meet behind closed doors in an attempt to establish the future of press regulation.
There has been no agreement between politicians and the newspaper industry since Lord Justice Leveson revealed his proposals earlier this year.
Among the outstanding issues being debated is the autonomy of any regulatory body, and the need for any code to be written independently.
The Labour party is banking on Liberal Democrat support in its argument that a crime and courts bill should be amended to include Leveson-compliant legislation.
The Lib Dems are free to vote on the issue however they wish, as press regulation was not part of the coalition agreement.