The Daily Mirror newspaper, citing unidentified sources, said the document revealed that Blair argued against Bush's suggestion of bombing the headquarters of the Aljazeera satellite channel in Doha, Qatar.
The Daily Mirror said its sources disagreed over whether it was a serious suggestion.
On Tuesday, civil servant David Keogh, 49, appeared on a charge of passing a document to Leo O'Connor, who formerly worked for a British lawmaker.
Keogh was charged with an offence under Section 3 of the Official Secrets Act relating to "a damaging disclosure" by a civil servant of information relating to international relations, between 16 April and 28 May last year.
O'Connor, 42, was charged under Section 5, which relates to receiving and disclosing the information.
Blair (L) is said to have urged
Bush not to bomb Aljazeera
O'Connor said he intended to plead not guilty. Keogh did not say how he intended to plead.
Judge Timothy Workman ordered both men to appear again at London's Bow Street Magistrates Court on 10 January.
Neil Clark, O'Connor's lawyer, said it was important for the court to see the contents of the document.
"As far as we are concerned, it needs to be disclosed because it is impossible to defend unless you know the case you are defending," Clark said outside court.
He said his client, who worked as a researcher for former Labour Party lawmaker Tony Clarke, had simply passed on the document hoping his employer would return it to the government - which he did.
Clark said he did not know what was in the document and could not confirm the Daily Mirror report.
Aljazeera's director general was
at a London seminar on Monday
Aljazeera director general Waddah Khanfar met Daily Mirror associate editor Kevin Maguire in a seminar held in London on Monday.
Khanfar said Aljazeera would stick to its aim of unbiased reporting and to its code of professional ethics.
Last week, legislator Adam Price asked Blair in a written parliamentary question "what information you received on action that the United States administration proposed to take against the Aljazeera television channel."
In his one-word reply published on Monday, Blair replied: "None."
White House spokesman Scott McClellan has called the newspaper's allegations "outlandish and inconceivable".