British newspaper The Daily Mirror reported that Bush told UK Prime Minister Tony Blair at a White House summit on 16 April 2004 that he wanted to launch military action on Aljazeera's headquarters in Doha, Qatar.
Blair is reported to have talked the American president out of any such action, but the British government has refused to give any comment on the truth of the Mirror's story.
"I have come to London in order to reach out to British officials, to investigate about the memo that some claim exists during the past week," Aljazeera managing director Waddah Khanfar said.
"It is a matter of deep concern for all of us in Aljazeera, and the Arab world and the media."
He said a delegation from the channel would deliver a letter to Blair on Saturday asking for an interview.
"The letter will say that Aljazeera has been working for the last nine years, it is the foremost forum of democracy in the Arab world, and therefore this news that we have heard is very concerning," Khanfar told BBC radio.
"It is of historical value to know exactly what has happened," Khanfar added.
The White House has said the allegation that Bush wanted to bomb Aljazeera is "so outlandish" it does not merit a response.
"People should know the facts about it. It is not a matter that can be brushed away or dealt with in very vague statements," Khanfar said.
Blair's spokesman said the prime minister's office had not yet received a formal request from Aljazeera for an interview, but the British government would be willing to talk to Aljazeera as it would to any other news organisation.
Blair is said to have talked Bush
out of attacking Aljazeera
"This is the first I suspect that Downing Street has heard of this request. It is somewhat short notice," he said.
"We are quite happy to talk to Aljazeera just as we are quite happy to talk to other broadcasters and media operations. In terms of who talks to them I think that depends on who is available and how much time he will give us to set up meetings."
Instead, British media have been warned that they face legal action under the Official Secrets Act if they report any further details from the memo.
Britain, which is prosecuting a civil servant and a parliamentarian's aide for leaking the secret memo, refuses to comment on its contents.
The Daily Mirror quoted one unnamed government official saying Bush's comments might have been a joke, but another unidentified source saying the president appeared to be serious.
Following the Mirror article, on Saturday a media safety network said the US and Britain had a duty to reassure journalists fearful of their safety in war.
Brussels-based International News Safety Institute (INSI) said in a statement that the Arabic satellite channel had attracted the anger of the US Administration for its reporting of the Iraq and Afghanistan wars and for broadcasting video footages from al-Qaida.
"Iraq is the most dangerous conflict for journalists in modern times with almost 100 new media staff dead in two and a half years. Thirteen of them incidents involving US troops," said ISNI director Rodney Pinder.
Aljazeera staff protested in Doha
and in overseas bureaus
"No one can guard and protect democracy by killing journalists," he said.
Journalists' fears that the report may not be so inconceivable are fuelled by previous incidents: a US missile attack on Aljazeera's Baghdad bureau in April 2003 which killed reporter Tariq Ayub, and the US bombing of Aljazeera's bureau in Kabul, Afghanistan in 2001.
"It is of very deep concern not only to Aljazeera journalists, but to people who trust Aljazeera as the most credible source of information in the Arab world," Khanfar said.
On Thursday, Aljazeera staff in Doha and overseas bureaus staged a symbolic protest over the report.
"The staff of Aljazeera have decided to organise on Thursday a symbolic sit-in in front of the headquarters of the channel in Doha and its overseas bureaus to protest against this news," said Aljazeera journalist Yusuf al-Shuli, who is also vice president of the Arab Association for the Defence of Journalists.
About 100 of the channel's journalists and employees signed a petition calling on the broadcaster's board of governors to hold an official inquiry into the allegations.