Lord Justice Leveson complained to the UK's top civil servant after a cabinet minister raised concerns about his inquiry into the press, it has emerged.
Education Secretary Michael Gove said in February that the debate around the hearings could erode freedom of speech.
That prompted the judge to contact Cabinet Secretary Sir Jeremy Heywood.
Lord Justice Leveson is understood to have been worried that if Mr Gove was speaking for the whole cabinet it could undermine his inquiry.
Mr Gove told a press gallery lunch at Westminster that there was "a chilling atmosphere towards freedom of expression which emanates from the debate around Leveson".
There were sharp exchanges between Lord Justice Leveson and Mr Gove when he subsequently gave his evidence to the inquiry in May.
Lord Justice Leveson's concern was based around the hearings into into the culture, practices and ethics of the press being a public inquiry that had been set up by the government, at taxpayers' expense.
However, the BBC understands that a headline in the Mail On Sunday - "Leveson's 'threat to quit' over meddling minister" - is not accurate.
BBC political correspondent Chris Mason said that at no point did Lord Justice Leveson threaten to resign.
When Mr Gove appeared in front of the inquiry at the end of May his exchanges with Lord Justice Leveson were tense.
At one point, the inquiry chairman said bluntly: "Mr Gove, I don't need to be told about the importance of free speech, I really don't."
A source close to Mr Gove said the education secretary had nothing to say about the story, said our correspondent.
Other sources emphasised that Lord Justice Leveson had always wanted to stress his independence from government, he added.
They pointed to his refusal to allow Culture Secretary Jeremy Hunt to appear before the inquiry earlier than originally scheduled.
This was when Mr Hunt faced revelations relating to his role in News Corporation's bid for BSkyB.