Annan told reporters on Friday that the new appointment will be announced soon.
"I will be naming a special representative shortly, and his duty station will be Baghdad," he said
Asked when, he replied, "Let's say in about a week, within a week."
Annan ordered all UN international staff to leave Iraq in October following two bombings at UN headquarters and a spate of attacks targeting foreign workers.
The first bombing on 19 August killed 22 people, including top UN envoy Sergio Vieira de Mello.
Since the withdrawal, Annan has dispatched senior UN officials on special assignments, including special adviser Lakhdar Brahimi - who helped put together the interim government that will take power on 30 June - and the UN elections chief Carina Perelli.
First senior UN official
The new UN envoy would be the first senior official permanently based in Iraq since October, but Annan has said he won't send large numbers of UN staff back to Iraq until the security situation improves.
"The United Nations is doing everything it can to help Iraqis prepare for free and credible elections in January next year"
UN Secretary General
Even though the current UN mission for Iraq works out of headquarters in neighbouring Amman, Jordan, Annan defended its effectiveness.
"The United Nations is doing everything it can to help Iraqis prepare for free and credible elections in January next year," he said. "It is vital that the interim government is given a real chance to exercise sovereignty in the meantime. I appeal to all concerned to do what they can to facilitate its formidable task."
Annan said Perelli's team helped put in place the legal framework for elections and a team of Iraqis was now being trained in Mexico to prepare for the elections.
Operating from Jordan
In addition to helping with elections, and eventually with the drafting of a new Iraqi constitution, Annan said UN staff in Amman have been operating in Iraq using local staff. The UN Development Programme, for example, is handling a $200 million programme with Iraqi staff, he said.
"We are doing whatever we can from Amman, and where necessary we do cross-border trips," he said. "We are trying to find creative ways to assist without necessarily overexposing our staff."
There are limits to what force
alone can do said the UN's Annan
The UN Security Council approved a major role for the United Nations after the handover of power, but made it contingent on security conditions, leaving it up to Annan to decide when staff should return.
He stressed that the electoral process and the political transition that the United Nations just helped with "are very critical activities."
"Quite frankly, if we are going to resolve the conflict in Iraq, it's through political reconciliation, it's through political work, it's through inclusive, participatory elections and the national conference that will be held next month" to bring all parts of Iraqi society together, Annan said.
"There are limits to what force alone can do; you have to go the political route," he stressed.
"So please do not underestimate efforts to get the political process going and to get the Iraqis engaged in talking to each other, democratically and otherwise. And I think that that is, in the long run, going to make much more difference than any force you can put in," Annan said.