Civil servant David Keogh, 49, and Leo O'Connor, 42, a lawmaker's former researcher, were charged in November with breaching the Official Secrets Act.
During a brief hearing at London's Central Criminal Court on Tuesday, judge Brian Barker set 25 April for their next pre-trial hearing. Both men are free on bail as they await trial.
Keogh, a former communications officer at the Cabinet Office, faces two charges under Section 3 of the Officials Secrets Act of making a "damaging disclosure of a document" without lawful authority.
O'Connor, who worked for former governing Labour Party lawmaker Tony Clarke, is charged with receiving the document.
They each face a maximum sentence of two years in prison.
O'Connor indicated at an earlier hearing that he intended to plead not guilty. Keogh has not entered a plea.
Details of the alleged document were reported by the Daily Mirror, which claimed the memo revealed details of a conversation between Bush and Tony Blair, the British prime minister, at the White House on 16 April 2004.
"I suspect it has more to do with saving the face of others abroad"
Leo O'Connor's lawyer
According to the newspaper, Blair argued against Bush's suggestion of bombing Aljazeera's headquarters in Doha, Qatar. The Daily Mirror said its sources disagreed on whether Bush's suggestion was serious or not.
Blair has said he had no information about any proposed US action against Aljazeera, and White House spokesman Scott McClellan called the newspaper's claims "outlandish and inconceivable".
O'Connor's lawyer, Neil Clark, on Tuesday said that he had seen the memo and that it did not violate national security.
"I suspect it has more to do with saving the face of others abroad," he said.