The denial came on Tuesday even as the British government turned down a request from Aljazeera for access to the memo containing the reported communication between Tony Blair and George Bush.
Blair's spokesman said: "We will reply properly in terms of any request to us, but it is not the practice and will not be the practice to release conversations between the prime minister and other world leaders."
"But what we can confirm is that the memo does not refer to bombing the Aljazeera station in Qatar, despite the various allegations," he said. "I am not aware of any suggestion of bombing any Aljazeera station."
He declined to say what was contained in the memo.
The Bush administration has criticised Aljazeera for what it considers inflammatory reports. Aljazeera has repeatedly denied US accusations.
Blair's spokesman also said that Downing Street would respond to the Aljazeera request, made on Monday by its lawyers under Britain's freedom of information laws, within 21 days.
A British newspaper reported last year that the memo of a Blair-Bush meeting in April 2004 detailed a proposal by Bush to bomb Aljazeera but said Blair had dissuaded him.
Peter Kilfoyle, a member of the British parliament, said last week he had been briefed on the memo by former MP Tony Clarke who had seen it, saying it had included a discussion of bombing Aljazeera.
Two men are facing trial on charges of leaking the memo.
The memo cast fresh doubts on motives behind past attacks on Aljazeera. In 2001, Aljazeera's Kabul office was bombed by the US, and in 2003 Aljazeera reporter Tareq Ayub was killed in a US strike on its Baghdad office.
The US has denied targeting Aljazeera.