Lord Justice Leveson is expected to break his silence on a controversial phone call in which he questioned David Cameron's commitment to his inquiry.
The judge contacted Cabinet Secretary Jeremy Heywood after Education Secretary Michael Gove expressed concern over the "chilling" effect the media standards probe was having on freedom of speech.
The Prime Minister subsequently said his minister had made an "important point" - prompting Lord Justice Leveson to seek assurances that the Government had not formed a view before his final report.
The call, which took place in February, was only revealed by the Mail on Sunday earlier this month.
In a telephone call with Cabinet Secretary Sir Jeremy Heywood he reportedly called for the Tory to be "gagged" and warned the inquiry was being undermined.
But inquiry sources have denied the newspaper's suggestion that the judge was ready to quit over the incident.
But it is understood that Lord Justice Leveson will make a statement explaining why it was appropriate to call Mr Heywood, rather than taking issue with the coverage.
Meanwhile, the inquiry is due to take evidence from senior journalists including Mail on Sunday political editor Simon Walters, the writer of the 'Threat to quit' story.
Philip Webster of the Times, Andy Grice of the Independent, and Channel 4 News presenter Jon Snow are also on the day's witness list.