In a statement posted on an Islamist website on Thursday, the author said 10kg of gold would also be given as a reward to anyone killing other officials including Bremer's deputy or UN envoy to Iraq al-Akhdar al-Ibrahimi.
"We in al-Qaida organisation are committed to a prize of 10,000 grams of gold to whoever kills Bremer, his deputy, the commander of American forces or his deputy in Iraq," the statement said.
It was not immediately possible to verify the authenticity of the statement, which said it would give the same reward for killing Annan and al-Ibrahimi.
"Whoever kills Kofi Annan, or the head of his delegation to Iraq, or his representatives such as al-Akhdar al-Ibrahimi, will get the same prize," said the statement, which was addressed to the Iraqi people.
Al-Ibrahimi is in Baghdad for talks on forming an interim Iraqi government in time for the US handover of sovereignty at the end of June.
The statement blasted the United Nations as a tool of "Crusaders" - a reference to the US-led occupation in Iraq - and accused it of surrendering Palestinians to Zionists.
The statement also offered one kg of gold to anyone who kills a US or British soldier, or civilian working for the US-led occupation, and 500 grams of gold for the killing of their allies such as Japanese or Italians.